







The difference between the ares of two rectangles 
20160609 

From Ingrid: I am trying to help my son with an area question.
I have the answer, from the solutions, but I cannot figure out how to teach him.
Question:
Two rectangles have lengths 13cm and 19cm respectively.
Their total area is 376cm squared.
If both their widths are whole numbers, what is the difference in their areas?
I know that this is solvable once I determine the widths of the rectangles ,
but how do I go about finding that?
Thanks for your help Answered by Chris Fisher and Harley Weston. 





Two pieces of rope 
20160521 

From Render: Fred cuts a 12 inch piece of rope. Then he cuts a second piece of rope that is 3/2 longer than the first piece. Is the second piece shorter or longer than the first piece? Explain. Answered by Penny Nom. 





The tens digit of a number is five times the unit digit 
20160519 

From sanjeev: The tens digit of a number is five times the unit digit. Find the number? Answered by Penny Nom. 





A rectangular field 
20160507 

From Jan: A rectangular field is 63m long and 21m wide. A fence of 2m in height is needed to fence the field and fencing is also required to divide the field in three square sections. There are three wooden gates measuring at 1.5m to the three sections of the field. What is the total surface area of the fence needed for fencing and diving the field? Answered by Penny Nom. 





A 3 hour river cruise 
20160506 

From Jan: A 3 hour river cruise goes 15km upstream and then back again.The river has a current speed of 2km/h.what is the boat's speed and how long was the upstream journey? Answered by Penny Nom. 





One million is six percent of what number? 
20160426 

From Colleen: One million is six percent of what number?
Thanks! Answered by Penny Nom. 





Dimes and pennies 
20160426 

From Renae: Charity has 42 more pennies than dimes. Hope has 7 times as many pennies than dimes. Hope and Charity have the same number of dimes. Together they have $5.46. How many dimes and pennies do each have? Answered by Penny Nom. 





External and interior angles of a regular polygon 
20160419 

From pearl: a polygon has n sides.The exterior angle is 8 times the interior angle
find the value of the interior angle
find the value of n Answered by Penny Nom. 





Mrs. Gibson has 3 children 
20160412 

From MJ: Mrs. Gibson has 3 children. The older ones are twins. The youngest one is 3 years
younger than the twins. If the sum of their ages is 102, how old is the youngest
one? Answered by Penny Nom. 





A road trip word problem 
20160410 

From Marc: While on a road trip I imagined this random word problem. Suppose I start a trip of 75 miles. My initial speed is 75 miles per hour. After every mile traveled I decrease my speed by one mile per hour. After the first mile I decrease my speed to 74 miles per hour and so on for each subsequent mile traveled. How long will it take to complete the 75 mile journey? Answered by Penny Nom. 





Biking and jogging 
20160317 

From alondra: Ricky went on a bike ride. After 6 miles he got a flat tire and had to jog home. He jogs 3mph slower than he bikes, so the jog took 1 hour longer than the bike ride. At what rate did he travel each way? Answered by Penny Nom. 





The perimeter of a rectangle 
20160317 

From Linda: Noel correctly adds the length of three sides of a rectangle and gets 88 cm her brother Ryan correctly adds the lengths of three sides of the same rectangle and gets 80cm. What is the number of cm in the perimeter of the rectangle Answered by Penny Nom. 





A word problem 
20160310 

From Sam: Jo is 10 cm taller than Ruth. Pam is 16cm taller than Ruth .Rod is 8cm taller than Pam.
How much taller than Jo is Rod? Answered by Penny Nom. 





A word problem 
20160227 

From KRK: amrutha thinks of a number, multiplies it by 5 & 6, devides the result by 3
and takes away the number first thought of to get an answer 36. find out
the number Answered by Penny Nom. 





Todd is 3 years older than his brother Jack 
20160213 

From Victoria: Todd is 3 years older than his brother Jack. If Jack is x years old and Todd is y years old, write a rule that relates their ages over time. When Jack is 28 years old, how old will Todd be? Answered by Penny Nom. 





38 is what percent of 400? 
20160207 

From chris: 38 is what percent of 400? Answered by Penny Nom. 





When will Scott and Jill have earned the same amount? 
20160204 

From kalia: Scott starts with $10 and earns $5 and hour. Jill starts with $40 and earns $3 and hour. when will the two have the same amount of money in the same hours? Answered by Penny Nom. 





The height of a triangle 
20160203 

From Brooklyn: How do I figure out the height of a triangle when it only tells me the base of he triangle? And vice versa. Answered by Penny Nom. 





Which term of the series 2+7+12+...is 152? 
20160201 

From francis: whice term of the series 2+7+12+...is 152? Answered by Penny Nom. 





Two increases of 20% 
20160127 

From Z: How do I find how many books are in a library given a problem like this... The number of books increase after buying 20% more in May. The number increased again by 20% after they were given 300 books. How many books did it start with?. Answered by Penny Nom. 





Two increases of 20% 
20160127 

From Z: How do I find how many books are in a library given a problem like this... The number of books increase after buying 20% more in May. The number increased again by 20% after they were given 300 books. How many books did it start with?. Answered by Penny Nom. 





A Max/Min problem with an unknown constant 
20160117 

From Guido: Question:
The deflection D of a particular beam of length L is
D = 2x^4  5Lx^3 + 3L^2x^2
where x is the distance from one end of the beam. Find the value of x that yields the maximum deflection. Answered by Penny Nom. 





A rectangular enclosure 
20160115 

From Amber: A rancher wants to use 300ft of fencing to enclose a rectangular area of 4400 square feet. What dimensions should the rectangle be? Answered by Penny Nom. 





A triangular shaped garden 
20160113 

From Demetrie: Dwayne's garden is triangleshaped with two equal sides and a third side that is 4 ft more than the length of an equal side. If the perimeter is 49 ft, how long is the longest side? Answered by Penny Nom. 





Sue's favourite number 
20160112 

From Maria: This is my son's homework. He is 7. Can you help?
Sue has a favourite number.
It is an even number.
It has 3 digits.
The digits add up to 15.
Find 10 numbers that could be Sue's number? Answered by favourite number. 





Three consecutive integers 
20160107 

From ronn: Three consecutive integers whose sum is 186 Answered by Penny Nom. 





Two transport companies 
20160106 

From Brynleigh: The Sugar Sweet Company will choose from two companies to transport its sugar
to market. The first company charges $5096 to rent trucks plus an additional fee of
$200.75 for each ton of sugar. The second company charges $5500
to rent trucks plus an additional fee of $175.50 for each ton of sugar.
For what amount of sugar do the two companies charge the same?
What is the cost when the two companies charge the same? Answered by Penny Nom. 





A ratio word problem 
20160106 

From Nina: The length and the width of the rectangle is in the ration 5:3. Its area is 375m2. Find its perimeter. Answered by Penny Nom. 





A troublesome word problem 
20151228 

From Linda: James is now 3/5 John's age. Three years ago, he was 1/2 John's age. Three years from now, he will be 2/3 John's age.
How old are they now? Answered by Penny Nom. 





A bus trip 
20151215 

From Michelle: I do not know what equation(s) should be used in order to obtain the answer(s) to this word problem.
A bus was rented for a trip, the cost was dived equally amongst the passengers. During the trip, someone mentioned that if there were 9 more passengers, they would have paid each 5$ less. Another mentioned that if there were 6 less passengers, they would have each paid 5$ more. What is the cost of renting the bus and how much must each passenger pay. Answered by Penny Nom. 





A word problem with percentages 
20151205 

From Caedryn: After giving 25% of her stickers away, May had 50% as many stickers as Rose. If they had 200 stickers altogether at first, how many stickers did Rose have? Answered by Penny Nom. 





The dimensions of a rectangle 
20150925 

From Erick: A rectangular strip of land has a perimeter of 124meters and an area of 385 square meters. Find its possible dimensions Answered by Penny Nom. 





32 golfers playing 6 rounds 
20150919 

From scott: i am looking for a schedule for 32 golfers to play 6 rounds and never play with the same person twice.
I made one for 28 golfers but i am struggling with 32. Answered by Victoria West. 





A word problem 
20150917 

From Suszanne: Multiplying a number by x yields the same result as dividing the number by 0.125. What is the value of x? Answered by Penny Nom. 





The weight of a pumpkin 
20150901 

From Lisa: A pumpkins weighs 10 pounds plus half of 10 pounds plus half it's own weight, what does the pumpkin weigh? Answered by Penny Nom. 





Working backwards 
20150827 

From Heather: Tom took a collection of tiles from a box. Sue took 13 and Bob
took half of those remaining. Tom had 11 left. How many did they start with? Answered by Penny Nom. 





Factor x^2 + y^2 
20150826 

From Jerome: Factor: x^2+y^2 Answered by Penny Nom. 





Four equations in 3 unknowns 
20150823 

From damien: solve:
S x U  T = 44
T  U x S = 36
U + T  S = 7
U x U / S = 4 Answered by Penny Nom. 





The distance between two boats 
20150726 

From mohammad: Two boats leave the same dock at the same time,one traveling due east at 10 mph and the other due north at 24mph,how many miles apart are the boats after 3hours ? Answered by Penny Nom. 





Mary, Julie and Peter when on a trip 
20150710 

From Edward: How do you solve and set up a problem where: Mary pays one third of the cost of a trip, Julie paid half of what Mary paid, and Peter paid the remaining $75, Answered by Penny Nom. 





A two digit number 
20150605 

From Madison: Trini took some photos. The number of photos she took is a two digit number.
The sum of the digits is 11. The tens digit is 3 more than the ones digit.
How many photos did Trini take? Answered by Penny Nom. 





A calculus optimization problem 
20150514 

From Ali: Given an elliptical piece of cardboard defined by (x^2)/4 + (y^2)/4 = 1. How much of the cardboard is wasted after the largest rectangle (that can be inscribed inside the ellipse) is cut out? Answered by Robert Dawson. 





A word problem 
20150508 

From JAMES: A businessman bought a number of similar articles for a total of sh. 6000. Three of the articles turned out to be defective with no resale value. He sold the remaining articles at 12.5% each above the cost price making a total profit of sh 480. How many articles had he bought? Answered by Penny Nom. 





A word problem with fractions 
20150423 

From Cecilia: if one third of a pole is red, one quarter is white and 15m is black what is the height of the entire pole Answered by Penny Nom. 





How many boats total are in the marina? 
20150415 

From Carla: In a marina, 3/4 of the boats are white, of the remainder 4/7 are blue, the rest are red. There are 9 red boats. How many boats total are in the marina? My answer is 84 because if 1/4 of the boats are divided into sevenths, that makes the whole marina a 28 part item. 3/28 are red so 84 is the total number of boats. My child thinks I am wrong. Answered by Penny Nom. 





A word problem with fractions 
20150409 

From Lorraine: If the numerator of a certain fraction is doubled and the denominator is increased by 1, the fraction becomes 1/2.
If the numerator of the original faction is squared and the denominator is decreased by 2, the fraction becomes equal to 1.
Let x be the numerator and let y be the denominator of the original fraction.
Write down two simultaneous equation in x and y.
Solve these equations to find two possible values for the given fraction. Answered by Penny Nom. 





Dealing cards to Melissa and Robert 
20150324 

From Karena: 92 cards in all. Melissa has 3 times as many cards as Robert. How many cards does Robert have? Answered by Penny Nom. 





The weight of two dogs 
20150317 

From Renee: Darlene's dog weighed 5 times as much as Leah's dog. Together, the dogs
weighed 84 pounds. How much did each dog weigh?
Write an equation and solve Answered by Penny Nom. 





Olivia and Ray walk to school 
20150312 

From Rebeccah: Olivia and Ray walk to school. Olivia walks 1/4 of a mile to school. Her walk is 2/3 of the distance that walks Ray to school. What is the total distance,in miles,that Ray walks to school? Answered by Penny Nom. 





Two sunflowers 
20150312 

From Maurice: Sam and sally planted two sunflowers.Each sunflower grows 1cm each day. Sally's sunflower is 4cm high. Sam's is 12cm high. How high will each sunflower be when Sam's sunflower is twice the height of Sally's? Answered by Penny Nom. 





An isosceles triangle and an arc 
20150218 

From Sreeharsha: The diagram shows an isosceles triangle ABC in which BC = AC = 20 cm, and angle BAC = 0.7
radians. DC is an arc of a circle, centre A. Find, correct to 1 decimal place,
(i) the area of the shaded region, [4]
(ii) the perimeter of the shaded region. [4] Answered by Penny Nom. 





A 330 foot long fence 
20150215 

From Marsha: I am putting up a fence 330 feet long and want to put the t post every 4 feet
how many t post do i need? Answered by Penny Nom. 





A word problem with fractions 
20150211 

From Omokayode: A vehicle tank was 3/5 full of petrol. When 21 litres of fuel was added it was 5/6 full. How many litres of petrol can the tank hold? Answered by Penny Nom. 





A fence post problem 
20150208 

From Nicole: In Susan's rectangular garden plot, she put 12 posts on the long sides
and 8 posts on the short sides. How many posts did she use altogether?
(The answer is not 40.) Answered by Penny Nom. 





The product of a 2digit number and a 3digit number 
20150206 

From Nathaniel: The product of a 2digit number and a 3digit number is about 50 000 what are the products Answered by Penny Nom. 





Jack and Jill climb two poles 
20150202 

From APRIL: Two vertical poles are 3 meters apart. Jack is climbing one pole while Jill climbs the other. If the distance between Jack and Jill is 5 meters, how much higher is Jill than John? Answered by Penny Nom. 





Russell is 6 years older than Samantha 
20150126 

From Kelli: Russell is 6 years older than Samantha.
In 4 years the sum of their ages will be 78. How old is Russell now? Answered by Penny Nom. 





A road around a garden 
20150125 

From hahha: a garden 150 m long and 80 m wide has a road 4 m wide all around on the out side find the cost of paving at the rate of 12 per s.q m Answered by Penny Nom. 





Largest cone in a sphere 
20150115 

From Alfredo: What is the altitude of the largest circular cone that may be cut out from a sphere of radius 6 cm? Answered by Penny Nom. 





A trip to Ottawa from Toronto 
20141222 

From Kristy: A trip to Ottawa from Toronto will take 4 1/2 hours. Assuming we are 2/3 the way there, how
much longer will the trip take? Answered by Penny Nom. 





A right triangle 
20141213 

From Katie: the shorter leg of a right triangle measures 2 feet less than the longer leg. the hypotenuse measure 10 feet. find all three sides Answered by Penny Nom. 





What is 20 and 3/5 of 10? 
20141126 

From Jeannine: What is 20 and 3/5 of 10? Question is written exactly this way.
Is this 20 3/5 times 10 (103/5 times 10), or is it 20 and (3/5 times 10)? Answered by Penny Nom. 





Mark's book case 
20141124 

From anne: mark has 312 books in his case. he has 11 times as many fiction books as non fiction books. how many fiction books does mark have? Answered by Penny Nom. 





An age related word problem 
20141118 

From Cole: Susan and Russell are brother and sister. Susan says that in two years she will be twice Russell's current age. Russell says that he's only three years younger than Susan. How old is each of the siblings? Answered by Penny Nom. 





Jason's speed 
20141031 

From jason: the speed of Jason is 12 times faster than everyone. The speed of Jason is 108mph. Write the equation and solve to find the speed of everyone else. Answered by Penny Nom. 





What is the speed of the boat in still water? 
20141030 

From Adam: The current in a stream moves at a speed of 2 km/h. A boat travels 38 km upstream and 38 km downstream in a total time of 3 hr. What is the speed of the boat in still water? Answered by Penny Nom. 





A 10foot piece of PVC pipe 
20141021 

From David: A plumber has a 10foot piece of PVC pipe. How many 9/5foot pieces can be cut from the 10foot piece ? Answered by Penny Nom. 





Three consecutive odd integers 
20141017 

From Maddy: 3 times the largest of three consecutive odd integers is 13 more than the sum of the other two. What are the integers? Answered by Penny Nom. 





A poorly worded question 
20141014 

From Marjorie: How do I figure out the following? Dylan's dog weights 12 times more than his pet rabbit. The dog and the rabbit weight 104 pounds. How much does Dylan's dog weigh? Would you explain in detail how I would arrive at the answer so I can convey same to my grandson who is in the 5th grade.
Thanks. Answered by Penny Nom. 





A quarter mile row of trees 
20141009 

From junna: a farmer would like to plant trees on one side
of his lot which is 1/4 of a mile in a length
His friend advised him that if he would plant
the trees 5 feet farther apart,he would need 44
fewer trees.If the farmer would take the advice,
how many trees would he plant? Answered by Penny Nom. 





A rectangle and a triangle 
20140927 

From rajesh: The perimeter of a rectangle is equal to the perimeter of a rightangled triangle of height 12 cm if the base of the triangle is equal to the breadth of the rectangle, what is the length of the rectangle? Answered by Penny Nom. 





A wire is bent to form a right triangle 
20140925 

From Lorena: A wire 24 dm is bent to form a right triangle. The ratio of the shorter leg to the hypotenuse is 3:5. Find the length of the longer leg? Answered by Penny Nom. 





How much did each dog weigh? 
20140916 

From Fred: LJ owned two dogs that weighed a total of 140 pounds. If one dog weighed 10 pounds more than the other, how much did each dog weigh Answered by Penny Nom. 





The average of 9 numbers is 45 
20140912 

From rizza: The average of 9 numbers is 45. If 90 and 88 are added to the set of numbers. What will be the resulting average? Answered by Penny Nom. 





The average age of a group of 10 students 
20140911 

From sujan: The average age of a group of 10 students was 20. The average age increased by 2 years when two new students joined the group . What is the average age of the two new students who joined the group? Answered by Robert Dawson and Penny Nom. 





The perimeter and diagonal of a rectangle 
20140910 

From niniha: the perimeter of a rectangle is 68cm.if the diagonal is 26, find its dimensions Answered by Penny Nom. 





A second grade word problem 
20140909 

From Beth: How do I explain to my second grader how to find the answer to the problem:
My tens digit is 8 more than my ones digit. My ones digit can not be zero. Answered by Penny Nom. 





Problem solving 
20140908 

From hubert: a car left the house and travelled at an average speed of 60 kph.how many minutes will it take for the car to reach the school which is 8 km away from the house Answered by Penny Nom. 





A secret number 
20140908 

From jai: it is smaller than half of 100, it is more than 4 tens and less than 5 tens, the tens digit is two more than the ones digit , together the digits have a sum of 6..... What is my secret number? Answered by Penny Nom. 





The sum of two numbers is 52 
20140901 

From Blake: The sum of two numbers is 52 and the difference is 10. What are the numbers? i used to be real good at this stuff? Answered by Penny Nom. 





Water usage in Ames 
20140829 

From Abigail: The City of Ames water treatment plant treats 7 million gallons of water per day on
average to meet water demands. Hypothetically, if water is withdrawn from a
groundwater system with an area of 51.6 square miles
(approximate area of Ames and surrounding area),
what is the depth of water in inches that would have to be added to
the groundwater system annually to replace the water that is withdrawn by the city? Answered by Penny Nom. 





Cutting a round cake so that it doesn't dry out 
20140826 

From James: I'm wondering if there's a simple way to calculate the area between two parallel chords of a circle equidistant from its diameter, or if I have the area, to find the distance between the two chords.
Here's my "problem". You may have heard of the way of cutting a round cake so that it doesn't dry out  make two parallel cuts (chords) the length of the cake, take the middle piece, then push the two pieces together.
So I know the area of a 12" cake, and I want say, exactly an eighth of the cake. How wide do I cut the centre piece?
Now to get even more difficult, the next day I want another eighth from the centre. How wide do I cut the next pieces, and so on...?
Thanks,
James Answered by Harley Weston. 





Distance, speed and time 
20140813 

From abdel: Mac walked to a park from the college at 5 km/h. 10 minutes later, Steve started
riding his bike at 15 km/h to the same park to meet Mac. They arrive at the same
time at the park. How far is the park from the college? Answered by Tyler Wood. 





A word problem with fractions 
20140801 

From nathanielcabalan: The denominator of a fraction is one more than the numerator. If the numerator is increased by three, the resulting fraction is one more than the original fractional. Find the original fraction. Answered by Penny Nom. 





A word problem concerning averages 
20140726 

From Bernie: The average weight of a team of children is 50kg, Todd who weighs 56 kg then joins the team. The average weight of the new team is 51. How many children in the original team? Answered by Penny Nom. 





4/9 of a set of story books cost Rs 630. 
20140709 

From YASIN: If 4/9 of a set of story books cost Rs 630. What will the rest of the set cost? Answered by Penny Nom. 





A word problem with fractions 
20140530 

From shadab: A container of milk is 4/5 full. When 10l milk is poured into it, the container becomes 9/10 full. What is the capacity of the container ? Answered by Penny Nom. 





A word problem with fractions 
20140523 

From Tanzeela: There are 1200 pupils in a school. 2/3 of them are girls. 1/4 of the boys are overweight.
How many boys are overweight? Answered by Penny Nom. 





Travelling upstream and downstream 
20140512 

From Mohanad: Howie Sorkin can travel 8 miles upstream in the same time it takes him to go 12 miles downstream. His boat goes 15 mph in still water. What is the rate of the current? Answered by Penny Nom. 





Mary's height as a percentage of Michael's height 
20140511 

From Lauren: Mary is 1.4m tall and her brother Michael is 1.2m tall.
Express Mary's height as a percentage of her brother's. Answered by Penny Nom. 





How many boards did the carpenter start with? 
20140508 

From Yanly: A carpenter has several boards of equal length. he cuts 3/5 of each board.
After cutting the boards, the carpenter notices that he has enough pieces
left over to make up the same length as 4 of the original boards.
How many boards did the carpenter start with? Answered by Penny Nom. 





A triangular chicken pen 
20140427 

From Cierra: Margaret has two lengths of fence, 20 meters and 24 meters, for two sides of a triangular chicken pen. The third side will be on the north side of the barn. One fence length makes a 75° angle with the barn. How many different pens can she build if one fence is attached at the corner of the barn? What are all the possible lengths for the barn side of the pen?
Not sure what they are asking here... please show step by step what to do! Thank you so much! Answered by Penny Nom. 





What was the selling price? 
20140425 

From Con: Apple built 40 32GB wifi iPads, gave away two in a contest, and sold the rest at two times the manufacturing price. If the company's total profit was $10,782, what is the selling price of one of these iPads? Answered by Penny Nom. 





What time was it when joe's brother passed him? 
20140425 

From Nathan: joe left home in his bike at 10:00 am, traveling 21 km/h. At noon, his brother set out after him on his motorcycle, following the same route. if the motorcycle traveled at 63 km/h, what time was it when joe's brother passed him? Answered by Penny Nom. 





Robyn and Shaun swim 
20140418 

From kajinthan: robyn swims four 35m lengths.shaun swims eight 15m widths. how much further does robyn swim?solve this maths Answered by Penny Nom. 





A circle is divided into three sectors 
20140417 

From atolagbe: the area of a circle is 154cm square. it is divided into three sectors such that two of the sectors are equal in size and the third sector is three times the size of the other two put together. calculate the perimeter of the third sector. take pi=22/7? Answered by Penny Nom. 





How fast did Jessica grow? 
20140410 

From jasmine: when she was 14 jessica was 5 feet, 4inches tall . at 18 she is now 6 feet, 2inches tall .how fast did jessica grow during this time Answered by Robert Dawson. 





Two rectangular prisms 
20140410 

From hannah: two rectangular prisms have a combined volume of 432 cubic feet Prism A has half the volume prism b has what are the volumes of prism a and prism Answered by Penny Nom. 





3/4lbs of nails fills a container 2/3 full 
20140404 

From Tyler: If 3/4lbs of nails fills a container 2/3 full, then how many lbs of nails will fill the container? Answered by Penny Nom. 





Shadows of a father and son 
20140402 

From esada: the father and son cast a shadow of 11 feet and 8 feet,respectively if the son is 4'8'' in height,how tall is the father? Answered by Penny Nom. 





A word problem with fractions 
20140326 

From lois: a man has a stack of boards, he cuts 3/5 off each board, after he cuts the boards he finds he has enough pieces left to make 4 boards the length of the original boards. how many boards did he start with. Answered by Penny Nom. 





Justin and his father went fishing 
20140326 

From Confused: Justin and his father went fishing and together caught 12 fish.
Three times the number of fish that Justin caught exceeds 12 by
as much as 5 times the number that his father caught exceeds 8.
How many fish did each catch? Answered by Harley Weston. 





Riding on a Ferris wheel 
20140321 

From Claire: A Ferris wheel has a radius of 72 feet and its center is 85 feet above the ground. At the top of the Ferris wheel, Sam is in the topmost car. If the Ferris wheel makes two complete revolutions per minute, how high above the ground will Sam be after 10 seconds? Answered by Penny Nom. 





Ms. Werenich's nickels, dimes and quarters 
20140319 

From London: Ms. Werenich has twice as many dimes as nickels and 4 more quarters than nickels. If she has $4.50, how many of each coin does she have? What would the let statements be of this problem and can you solve it? Answered by Penny Nom. 





Find two numbers with a sum of 8 and a difference of 4 
20140319 

From Elisabeth: Find two numbers with a sum of 8 and a difference of 4. Let x be the greater number and y be the lesser number. Answered by Penny Nom. 





Three consecutive whole numbers 
20140313 

From Abhishek: Three consecutive whole numbers are such that if they be divided by 5,3 and 4 respectively, the sum of the quotient is 40. What are the numbers? Answered by Chris Fisher. 





The ratio of boys to girls is 5:3 
20140310 

From jane: The ratio of the number of boys to the number of girls in the concert hall is 5:3. After additional 28 boys entered the concert hall, the ratio of the number of boys to the number of girls become 3:1 How many girls are their in the concert hall? Answered by Penny Nom. 





A word problem 
20140309 

From Joanne: Ashley weighs 5kgs more than Joyce. Their total weight is 41 kgs. What is the weight of Ashley? Answered by Penny Nom. 





A word problem 
20140223 

From Anh: The Texas State Legislature is comprised of state senators and state representatives. The sum of the number of senators and representatives is 181. There are 119 more representatives than senators. How many senators and how many representatives make up the Texas Legislature? Answered by Penny Nom. 





A word problem with fractions 
20140223 

From alex: In a certain fraction the number by n the denominator is greater than the number by3.If 2 is added to both the numerator and denominator ,the fraction is increased by 6/35..Find the fraction. Answered by Penny Nom. 





A fountain surrounded by a walk 
20140218 

From Maddie: A square Water Fountain is Surrounded by a walk 2 yards wide.
If the Area of the Fountain is 2/3 of the total area of the Fountain and the Walk.
What are the Outside Dimensions of the Walk Answered by Penny Nom. 





Paul is making banana bread 
20140217 

From John: Paul is making banana bread. The number of cups of bananas he uses is proportional to the number of loaves of bread. Paul uses 11 1/4 cups of bananas to make 5 loaves of bread. Which equation represents the relationship between c, the number of cups of bananas, and b, the number of loaves of bread?
A) C=4/9 b
B) C=2b
C) C= 2 1/4 b
D) C=5b Answered by Penny Nom. 





Some mixed nuts 
20140212 

From Andrew: How many kg of mixed nuts that contain 30% peanuts must Paul add to 6kg of mixed nuts that contain 38% peanuts to make a mixture that contains 33% peanuts? Answered by Penny Nom. 





A word problem 
20140211 

From cyril: In a rectangle,the length is 1.5 times the breadth.if the length is shortened by 3 m and the breadth is lengthened by 3 m, the rectangle will be a square. Calculate the dimensions of the rectangle. Answered by Penny Nom. 





Pizza for 24 
20140207 

From Delaney: if 8 people eat 2/3 of a honey chicken pizza how many pizzas are need to feed 24?
How is this problem solved. Thank you! Answered by Penny Nom. 





The dimensions of a room 
20140201 

From jenna: The length of a rectangular room is 2m more than the width. Find the dimensions if the perimeter of the room is 34m Answered by Penny Nom. 





A bizarre percentage problem 
20140129 

From matthew: by what percent was the child's sodium level beneath the normal range?
the child's sodium level was 107 where the normal is 136145 Answered by Harley Weston. 





Problem solving 
20140124 

From ngozi: There are 4 children in the Owens family. Jamie 1 1/2 times as all as Kelly and he is 6 inches taller than Olivia. Sammy is 56 inches tall, which is 2 inches taller than Olivia. Find Jamie's height Answered by Penny Nom. 





Kate, Tess and Nina 
20140123 

From Sam: Kate is 16 yrs. younger then Tess. Nina is 8 yrs.older then Kate. The sum of their ages is 189. How old is each? Answered by Penny Nom. 





A word problem involving fractions 
20140123 

From Pamela: John put 1/4 of his flowers in a vase
He gave 1/2 to of the flower to his wife
He gave 1/5 of the flowers to his daughter
He has 8 flowers left
How many flowers did John start with Answered by Penny Nom. 





Reducing the area of a parking lot 
20140119 

From Robin: The school is reducing the area of its 20yd by 50yd parking lot by removing a strip at one end of the parking lot and another strip of the same width from one side. The new area of the parking lot is 504 said yes. Find the width of the removed strip Answered by Penny Nom. 





Mixing water and wine 
20140119 

From manish: a man mixes three part of water to one part of wine.When he consumes
one part of mixture he realise that the drink is too dilute and hence adds one part of
wine to the remaining quantity what is the ratio of water to wine in the new mixture. Answered by Penny Nom. 





Mark's books 
20140118 

From Jason: Mark has 312 books in his bookcases he has 11 times as many fiction books as nonfiction books how many fiction books does mark have?
26 212 286 301 Answered by Penny Nom. 





$9.50 in coins 
20140115 

From dana: you have $9.50 in coins. it has twice as many nickels as quarters and three times as many dimes as nickels. how many of each coin do you have? Answered by Penny Nom. 





Five cubes 
20140115 

From Bob: Rick has five cubes. When he arranges them from smallest to largest, the difference between the heights of any two neighbouring cubes is 2 cm. The largest cube is as high as a tower built from the two smallest cubes. How high is a tower built from all five cubes? Answered by Penny Nom. 





Watching a bouncing ball through a window 
20140115 

From Bob: A ball falls from the roof, at a height of 10m. After each impact on the ground it bounces back up to 4/5 of its previous height. How many times will the ball appear in front of a rectangular window whose bottom edge is at a height of 5m, and whose top edge at a height of 6m? Answered by Penny Nom. 





Radio direction finders 
20140109 

From Nathan: Radio direction finders set up two points A and B, which are 2.5 miles
apart on an eastwest line. From A, it is found that the bearing of a
signal from a radio transmitter is N36.33 degress E, while from B the
bearing of the same signal is N53.67 degrees W. Find the distance of
the transmitter from B. Answered by Penny Nom. 





Two tuna boats 
20140109 

From amanda: Two tuna boats start from the same port at the same time, but they head in opposite directions. The faster boat travels 10 knots per hour faster than the slower boat. At the end of 8 hours, they were 272 nautical miles had each boat traveled by the end of the 8 hour period? Answered by Penny Nom. 





4 children 
20131231 

From hope: 4 children; Peter is 7 years old & is 4 years younger than Dave. Dave is 9 years older than Paul. Paul is 11 years younger than Frances. Please list the children in order from oldest to youngest?!
thank you and anxiously await your answer, Hope Answered by Penny Nom. 





A word problem 
20131208 

From Malissa: I am attempting to help my son with his math word problem, please help thank you .
Kylie and Ethan kept scrapbooks of their grandfather's stories from world war II. Kylie has 6 more than half the number of pages Ethan has. If Kylie has 21 pages in her scrapbook, how many pages are in Ethan's scrapbook? Answered by Penny Nom. 





Problem solving with fractions 
20131203 

From Jennie: Paul has 2/3 as many postcards as Shawn. Shawn has 3/5 as many postcards as Tim.
If the 3 boys have 280 postcards, how many more postcards does Tim have than Paul? Answered by Penny Nom. 





People on a bus 
20131128 

From jeric: 3/10 of the passenger in a bus were men, 2/7 of the remainder were women and the rest were children, if there were 50 passengers in the bus, how many more children than women were there? Answered by Penny Nom. 





Problem solving 
20131126 

From Moira: Amy has £5 more than Ben. Ben has twice as much as Chris. In total they have £20 how much do they each have Answered by Penny Nom. 





Three roommates share the rent 
20131123 

From Cortlin: Because of different bedroom sizes, three roommates decide to split the rent this way:
Roommate A pays 75% as much as B does, and C pays 40% as much as B does.
What fractional part and percent of the rent does each roommate pay? Answered by Penny Nom. 





A ratio problem 
20131031 

From indu: students of a school have been into 2 groups in the ratio 6:11, if the group has 870 students, how many students are there in all the school? Answered by Penny Nom. 





Tim is standing in a hole 
20131023 

From Marvel: Tim is standing in a hole that is 4 feet deep.
Ben asks him how much deeper is he going to dig the hole.
Tim replies he will dig to the level that is 4 feet 2 inches deeper
and that then the top of his head will be the same distance below
ground level that it is now above. How tall is Tim? Answered by Penny Nom. 





Together, Tom and Max have 72 football cards 
20131021 

From Maureen: Together, Tom and Max have 72 football cards. Tom has 2 more than 4 times as many cards as Max has. How many football cards does Tom Have? Answered by Penny Nom. 





Peter bought pizza and drinks 
20131019 

From sd: Peter spent $30 on pizza and 3/4 of the remainder on drinks. He has 2/9 of the original amount left. How much had he at first? Answered by Penny Nom. 





What the dog weighs 
20131017 

From linda: Sam has a dog and rabbit together they weigh 104 lbs the dog weighs 12 times more then the rabbit what is the dogs weight Answered by Penny Nom. 





Two bikers race on a circular track 
20131003 

From bryan: two bikers race on a circular track. biker a can circle the track in 8 minutes, and biker b can circle the track in 6 minutes. From the start of the race, how many minutes will it be before biker b overtakes biker a. Answered by Chris Fisher. 





Problem solving 
20131002 

From naomi: My son having trouble a math problem please help with this question a bag of cough drops contains 36 drops. the fraction of each flavor is shown in the table strawberry 5/12 honey 1/12 cherry 1/6 mint1/9 and lemon 1/4 which flavor is the greast in the bag Answered by Penny Nom. 





A pool, a school, a park and home 
20130924 

From Selena: The distance from the park to the pool is the same distance as the distance from your house to school. The school is between the pool and your house. Prove that the distance from the park to the school is the same distance from the pool to your house. Answered by Robert Dawson. 





A sequence of operations, in order 
20130920 

From jen: multiply 46x23
add 342
divide by 70
subtract 5
I not sure what the answer is..i need to know the answer..thanks.. Answered by Penny Nom. 





A concrete walk around a pool 
20130918 

From poornima: circular Swimming pool is surrounded by a concrete walk 4 feet wide, if the area of the walk is 11/25 of the area of the pool, then the radius of the pool in feet is Answered by Penny Nom. 





A garden path 
20130906 

From mary: garden path has 8 white slabs, four of the slabs are one third grey, what area of the path is grey Answered by Penny Nom. 





A word problem 
20130905 

From Thomas: I'm trying to help my 9th grade child with their homework. The problem is the
Length of a rectangle is twice as long as it is wide. The perimeter is 68m. Find
It's length and width Answered by Penny Nom. 





A two digit number 
20130904 

From JEFFERSON: The sum of the digits is 6. When the digits are interchange, the new number represented is 3 time the 10 digit of the original number. Find the original number? Answered by Penny Nom. 





How many nickles do you have? 
20130904 

From Monica: You have 15 more dimes than nickels. If you have $2.55, how many nickels do you have? Answered by Penny Nom. 





Golden Ratio 
20130826 

From Mark: Please Help. I'm trying to help my Child and I have no clue on this math question.
Rectangular shapes with a length to width ratio of approximately 5 to 3 are pleasing to the eye.
The ratio is know as the golden ratio. A designer can us the expression 1/3(5w) to find the
length of such a rectangle with width 6 inches. Answered by Robert Dawson and Penny Nom. 





A mixture problem 
20130811 

From MJ: How many liters of pure acetic acid must be mixed with 3 liters of a 30% acetic acid to obtain a mixture of 65%? Answered by Penny Nom. 





A mixture problem 
20130729 

From Lucy: Hi,
For the following question:
Ten pounds of mixed nuts contain 50 percent peanuts. How many pounds of peanuts must be added so that the final mixture has 60 percent peanuts?(A) 2.5 (B) 5 (C) 6 (D) 10 (E) 12.5,
my math book gives my the following explanation: Try choice (C): 6 pounds of peanuts. The original 10pound mixture contained 50 percent peanuts, or 5 pounds. Now you have 11 pounds of peanuts in a 16pound mixture, more than 60 percent. This result automatically eliminates choices (D) and (E) as well.Why would this result automatically rule out D and E? How can you tell?
Thank you for taking the time to answer my question. Answered by Robert Dawson and Penny Nom. 





A word problem 
20130729 

From Gontsejalo: Your firm held a dance competition. 900 people attended the dance competion.The cost of admission was 20rand per person and 30,50rand per couple.Twice as mant 20rand tickets as 30,50rand tickets were sold.find the amount of money obtained from the tickets sales Answered by Penny Nom. 





Ann has a bag of marbles. 
20130725 

From Carmen: Ann has a bag of marbles. she gave one half to her friend Tina and then one third to her friend Tom. Now left with 15. How many did she had originally? Answered by Robert Dawson and Penny Nom. 





150 litres has been drawn from a tank 
20130714 

From henry: When 150 litres has been drawn from a tank, it is 3/8 full, how many litres will the tank hold? Answered by Penny Nom. 





Diego and his dog 
20130709 

From William: john went hunting and walked at a speed of 4 km/h. one hour later, Diego and his dog went to meet john with a speed of 6 km/h and the dog was running between john and diego until they meet up with a speed of 18 km/h. After Diego meets john, how much distance did the dog run? Answered by Penny Nom. 





Two numbers whose difference is 16 
20130608 

From Johan: Two numbers whose difference is 16 and whose sum is 120 Answered by Penny Nom. 





The percentage of fat in a container of yogurt 
20130517 

From Katy: There is a question that I' having trouble with. It says: "A container of yogurt
contains 228 g of water, 54 g of carbohydrates, 12 g of protein and
6 g of fat, what percentage of the yogurt is fat?" How do you convert 6 g
into percentage? Answered by Penny Nom. 





A word problem 
20130503 

From Shaneaya: Keikio spent the day bird watching and counted 34 more birds in the morning than in the afternoon. If she counted a total of 76 birds, how many birds did she count in the afternoon? Answered by Penny Nom. 





The dimensions of a rectangle 
20130319 

From stephanie: the length of a rectangle is 5m more than twice its width, and the area of the rectangle is 88m^2 find the demensions of the rectangle Answered by Penny Nom. 





If 4 cooks can bake 8 pies in 6 hours????? 
20130318 

From Kenneth: Hello:
I want to determine which quantities are directly and inversely proportional in order to determine the answer for the following:.
If 4 cooks can bake 8 pies in 6 hours, 2 cooks can bake how many pies in 4 hours?
Answer: 2 2/3 pies
Can someone fully explain what I need to know in order to determine what is directly and inversely proportional in the example above?
I thank you for your reply. Answered by Robert Dawson. 





Driving a rental car 
20130313 

From teresa: Driving a rental car x miles cost y= 0.25x + 25 dollars.
(a) How much would it cost to rent the car but not drive it?
(b) How much does it cost to drive the car 1 additional mile?
(c) What is the yintercept of y= 0.25x + 25? What does it represent?
(d) What is the slope of y= 0.25x + 25? What does it represent? Answered by Penny Nom. 





100 animals 
20130225 

From Jessica: You have exactly $100.00 to spend. You must get 100 animals.
The chicks cost $0.10 each.
The pigs cost $2.00 each.
The sheep cost $5.00 each.
You must get some of each animal.
How many of each animal can you get? Answered by Penny Nom. 





A trig word problem 
20130218 

From Amy: Susan notices an unusual rock formation at an angle of 30 degrees to the right of her direction of travel as she is white water rafting. as she continues in a relatively straight path for 20 m, the rock formation appears to be at 45 degrees to the right. she cotninues until the rock formation is directly to her right. how far is she fromt he rock formation? Answered by Penny Nom. 





Chocolate bars and puzzles 
20130215 

From sandy: Alan bought a box of puzzle and two bar of chocolate for $28.
Jan bought 3 boxes of puzzle and a bar of chocolate similar to
Alan for $69.
a) Find the cost of a box of puzzle
b) Find the cost of a bar of chocolate Answered by Penny Nom. 





A word problem involving toys 
20130214 

From sandy: Each boy gets 5 toys.Each girl gets 3 toys.There are 150 pupils.
The boys had 74 more toys than girls.
How many boys?
How many girls? Answered by Penny Nom. 





The height of an aerial 
20130212 

From ASIT: A vertical aerial stands on a horizontal ground. A surveyor positioned due east of the aerial measures the elevation of the Top as 48 degree. He moves due south 30metre and measure the elevation as 44 degree. determine the height of the aerial Answered by Penny Nom. 





A cubical shipping container 
20130212 

From Chantel: The length, width and height of a cubical shipping container are all
decreased by 1.0 ft, thereby decreasing the volume of the cube by
37 ft3(feetcubed) What was the volume of the original container?
(recall: volume of cube with a side length x=x3) Define the variable,
write a quadratic equation and solve by factoring. Answered by Penny Nom. 





Brian is x years old 
20130206 

From Sabrina: Brian is x years old.
Peter is 4 years older than Brian.
Amy is 2 years younger than Brian.
The total of their ages is 26 years.
Work out the value of x. Answered by Penny Nom. 





The area of a rectangle 
20130129 

From Bali: if the length of the
rectangular field is decreased by 5m,
its area is decreased by 70 sqm. if the
width is increased by 6m, the area is
increased by 180 sqm. determine the
length and width of the rectangular
field? Answered by Penny Nom. 





We have 2 teams of 6 couples each that play 6 games 
20130125 

From Denise: We put together a game night where we have 2 teams of 6 couples each that play 6 games. We haven't been able to figure out an arrangement that allows each couple to play each game with a different couple from the opposite team (i.e. Team A couples play every game with a different couple from Team B). Is this possible? It works with 2 teams of 5 couples each. Answered by Chris Fisher. 





Use 9,10,6,8, and 4 to make 10 
20130125 

From Able: How do you calculate using BEDMAS 9,10,6,8,4 to equal 10 Answered by Penny Nom. 





A geometry word problem 
20130124 

From Matthew: "G", "A" and "B" are collinear. "A" is between "G" and "B". "GA" Is 14 less than 3 times "AB". "GB"=46 Find "GA"
How would you solve this? Answered by Penny Nom. 





How many students have neither brown hair or hazel eyes? 
20130120 

From Julie: There are 28 students in a class. 15 have brown hair, 17 have hazel eyes, and 10 have both. How many students have neither brown hair or hazel eyes? Answered by Penny Nom. 





Maximize profit 
20130119 

From Chris: A firm has the following total revenue and total cost function.
TR=100x2x^2
TC=1/3x^35x^2+30x
Where x=output
Find the output level to minimize profit and the level of profit achieved at this output. Answered by Penny Nom. 





A balance puzzle 
20130114 

From Emily: I'm stuck on this problem and feel that it can't work! The problem is: there is a door with a balance scale on it. In order to open the door, you have to use the 5 weights to balance the scale. On the left side you have 2 boxes to place the weights and on the right side you have 3. You're 5 weights are as follows: 1lbs, 2lbs, 3lbs, 4lbs, 5lbs. How do you place the weights so that the scale is balanced? Answered by Penny Nom. 





A triangular island 
20121229 

From Udit: A long time ago Mr Gibson found an island shaped as a triangle with three straight shores of length 3 km,4 km and 5 km. He declared an 'exclusion zone' around his island and forbade anyone to come within 1 km of his shore. What was the area of his exclusion zone? Answered by Penny Nom. 





Increasing the size of a gift box 
20121227 

From Tehmas: The dimensions of a gift box are consective positive integers such that the height is the lowest integer and the length is the greatest integer. If the height is increased by 1cm, the width increased by 2 cm, and the length increased by 3 cm, then a larger box is constructed and the volume is increased by 456 cm^3. Determine the dimensions of each box. Answered by Harley Weston. 





A parabolic bridge 
20121209 

From Elizabeth: 1) The figure below shows a bridge across a river. The arch of the bridge is a parabola and the six vertical cables that help support the road are equally spaced at 4m intervals. Figure B shows the parabolic arch in an xy coordinate system, with the leftend of the arch at the origin. As indicated in Figure B, the length of the leftmost cable is 3.072 m.
I'm suppose to find the (xh)^2=4a(yk) equation for this word problem and I really do not know where to begin.
Afterwards, I need to find the lengths of the other cables and the maximum height of the arch of the road as well which I am very confused about Answered by Penny Nom. 





Mark has 312 books 
20121207 

From paul: Mark has 312 books. He has 11 times as many fiction books as non fiction books. How many fiction books does he have? Answered by Penny Nom. 





A function problem 
20121118 

From nahla: f: IN > IN
n > f(n)
for every n that belongs the IN : fof(x) = 4n  3
and for every n that belongs to IN f(2^n) = 2^(n+1) 1
Calculate f(993) Answered by Penny Nom. 





A path around a pond 
20121116 

From bailey: hi there,
A circular pond is surrounded by a path 1 metre wide.
The area of the path is 1/4 of the area of the pond.
Find the radius of the pond.
Thanks Answered by Penny Nom. 





How much should I price the earrings? 
20121113 

From Sharon: I want to sell some earrings and make a $12.00 profit on them I have to pay a
35% commission on them. How much should I price the earrings? Answered by Penny Nom. 





What's your secret? 
20121111 

From ryan: Tuscan school has a fair. At the fair, Pia plays "what's your secret?
The game starts with 3 players who are told the same secret.
Each of those 3 players tells another 3 player, and so on.
At the end of the 3rd round, everyone who knows the secret
will compare what they have heard. What number in exponent form
represents the number of people who know the secret after 3 rounds?
How many people is that?
Thank you very much.
P.S. I got 3 cube. which is 27
But when i map it out I end up with 39. Answered by Penny Nom. 





Joe and Chris each bought a six pack of cola 
20121101 

From Loulou: Joe and Chris each bought a six pack of cola. Joe gave 2/3 of his away and Chris gave half as many as Joe. how many more colas did Chris have than Joe Answered by Penny Nom. 





Filling a box with wood chips 
20121031 

From leeAnne: Each bag of wood chippings will fill 4m3 how bags would be needed?
Volume of box is 572 cm3
L=11CM
W= 6.5CM
H=8CM Answered by Penny Nom. 





Frosting a three layer cake 
20121030 

From johnathan: Each layer of a 3 layer cake is a cylinder with height 7.5 cm. The bottom layer has diamegter 25 cm. The middle layer has dimegter 22.5 cm. The top layer has diameter 20 cm. The surface of the cke is frosted. What area of the cake is frosted. I get 1695.56 but the answer in the book is 2081.3 Answered by Penny Nom. 





birdhouse in the shape of a rectangular prism 
20121029 

From Tiffany: Hello, I am Tiff M. from NYC.
I was solving a math problem about adding,subtracting,multiplying
or dividing fractions and mixed numbers. I am not getting this
question below.
* Laura is building a birdhouse in the shape of a rectangular prism.
The base of the birdhouse has an area of 5 square inches. The
height of the birdhouse is 2 7/12 inches. Laura calculated the
volume of the bird house to be 10 7/12in. Is she correct?
If not, what did she do wrong? Answered by Robert Dawson. 





Forming an algebraic expression 
20121027 

From ashley: A sidewalk has a constant width W and comprises several short sections having lengths
12, 14,and 10 feet. How do I find the simplified expression that gives the number of square feet of sidewalk? Answered by Penny Nom. 





Whites and Sulphurs butterflies 
20121019 

From Arlene: The Whites and Sulphurs are one major family of butterflies. There are about 720 varieties. Eleven times more Whites and Sulphurs live outside North America, mostly tropical Asia and Africa, than live inside North America. How many of this family of butterflies live in North America? How many live in the rest of the world? Answered by Penny Nom. 





Walking home from school 
20121015 

From margie: My sister can walk from school to home in 40 minutes. I can walk from school to home in 30 minutes. Today I stayed for some extra help, and my sister was already 2/5 of the way home when I started. If I walk at my usual speed, can I catch my sister before she gets home? If yes exactly what fraction of the trip have we covered when I catch her? If no exactly what fraction of the trip have I covered when my sister gets home? Answered by Penny Nom. 





A four digit number 
20121009 

From cyndi: find this 4 digit number: the tens digit is 1/3 of the hundreds digit; the 2 digit number formed by the tens and ones digits i the largest prime number smaller than 40; the sum of all 4 digits is the same as the number of face on an icosahedron ? what is the number? Answered by Penny Nom. 





A problem that yields a linear equation 
20121007 

From Eshraj: one fourth of a whole number is three more than one fifth of the next whole number.find the whole number Answered by Penny Nom. 





How many oranges? 
20121006 

From Rodger:
Question from Rodger, a teacher:
How Many Oranges?
Marjorie, Colleen, and Bob picked oranges together. They were tired after picking a large number of oranges and so fell asleep. Marjorie woke first and decided to take her third of the oranges and head home. She counted the oranges, and found that the number was divisible by 3 if she took one of the oranges first. Marjorie took one orange and then took onethird of the remaining oranges. She left quietly.
Bob awoke a short time later, noticed that Colleen was sleeping, and presumed Marjorie had gone for a walk. He decided to head home because he wasn't feeling well. Not realizing that anyone had left, he counted the oranges and found that the number of oranges was two more than a number that could be easily divided by 3. So he took the two extra oranges and then onethird of what was left. He left without waking Colleen and without waiting for Marjorie to return.
Colleen finally awoke and wondered where her friends had gone. She assumed they were both busy somewhere nearby. Before she left, she counted the oranges and was surprised at how small the number was. She found that the number of oranges was one more than a multiple of three, so she took the extra orange and one third of those remaining.
1. What was the total number of oranges the friends picked?
2. How many oranges were left behind when Colleen departed?
3. Is more than one answer possible for the total number of oranges? If so, what other numbers are possible? Explain.
4. Based on the values you found in problem 3, determine a reasonable solution to the problem. Explain your answer.
5. Is it possible that five oranges remained after Colleen took her share? Explain.
6. Could there have been six oranges left after Colleen departed? What about 46 oranges initially? Explain
7. Find a pattern that gives all the possible numbers of oranges that the friends picked. Explain your pattern
5. Is it possible that five oranges remained after Colleen took her “share”? Explain.
6. Could there have been six oranges left after Colleen departed? What about 46 oranges initially? Explain
7. Find a pattern that gives all the possible numbers of oranges that the friends picked. Explain your pattern Answered by Penny Nom. 





The dimensions of a rectangle 
20120912 

From Becky: A rectangle has an area of 48 square inches and perimeter of 32 inches. Find the dimensions of the rectangle. Answered by Penny Nom. 





A 2digit number 
20120823 

From patty: Write the 2digit number that matches the clues.
My number has a tens digit that is 8 more than the ones digit. Zero is not one of my digits.
My number is Answered by Penny Nom. 





Kirkman schoolgirl problem 
20120818 

From Anthony: need to have the number from 115 in 6 rounds of 3 numbers without the numbers be repeating in the same row . eg round 1
1 2 3
4 5 6
7 8 9
10 11 12
13 14 15
2nd round
1 4 7
10 13 2
5 8 11
14 3 6
9 12 15 Answered by Chris Fisher. 





Problem solving 
20120815 

From Sugavanas: If length of a rectangle exceeds its width by 5 m. if the width is increased by 1m and the length is decreased by 2 m, the area of the new rectangle is4 sq m less than the area of the original rectangle. Find the dimensions of the original rectangle. Answered by Penny Nom. 





A 4 digit number 
20120809 

From May: The number is given as ABCD. The first digit is a quarter of the last digit. The second digit is one less than the first digit.
When the number ABCD is multiplied by four its digits appear in the reverse order. None of the digits are the same. What is the number. Pleas help because my child need help and I can not do this. Thank you. Answered by Penny Nom. 





The difference between two numbers is 7. 
20120809 

From May: The difference between two numbers is 7. When the two numbers are multiplied the answer is 60. How do I work out the two numbers,I tried solving for one unknown and substitution and can not do it. Pleas show me how to do this. Answered by Penny Nom. 





A garden in the back yard 
20120804 

From Lucy: Your boss says that his wife has put an 18 × 51 foot garden in along the whole back end of their back yard. He says that this has reduced the backyard lawn area by 24%. What are the total dimensions of his back yard? What are the dimensions of the remaining lawn area? I found this question on purplemath(http://www.purplemath.com/modules/percntof3.htm). I still don't understand how to solve it. Can you walk me through the process please?
Thank you in advance for taking the time to answer my question. Answered by Penny Nom. 





John's electronic store 
20120725 

From Jora: Electronic Store
John opened an electronic store in December. During his first month,
He sold 10 LCD TVs and 20 Plasma TVs. His income during that
month was $12800. In January, he sold 25 LCD TVs and 40 Plasma
TVs for an income of $27600.
In February he projects to sell 30 LCD TVs and 50 Plasma TVs.
If John expenses are $28900 in February, how much money will he
have after paying the expenses? Answered by Penny Nom. 





Romeo and Juliet live 40 miles apart 
20120518 

From Abigaíl: Romeo and Juliet live 40 miles apart. Romeo jogs 8mph, while Juliet “fast walks” at 4mph. They leave their houses at the same time and journey toward each other.
a) How many hours after they start will they meet?
b) Approximately how many miles from Romeo’s house is their meeting point? Answered by Penny Nom. 





Math, time and rate 
20120518 

From Abigaíl: Romeo and Juliet live 40 miles apart. Romeo jogs 8mph, while Juliet “fast walks” at 4mph. They leave their houses at the same time and journey toward each other.
a) How many hours after they start will they meet?
b) Approximately how many miles from Romeo’s house is their meeting point? Answered by Penny Nom. 





Cycling and running 
20120507 

From liz: a biathlete travels 20 miles in 2.25 hours. She cycles part of the way at 12 mph and runs the rest at 5 mph. How far did she run? Answered by Penny Nom. 





A puzzle with a triangle and 57 
20120425 

From sharon:
Question from sharon, a parent:
We have been battling with this for days and cant find any solution 
Using each of the following numbers once, fill all the spaces in the triangles so that each side of the triangle adds up to 57
numbers are 11,12,13,14,15,16,17,18,19
diagram is 
Any ideas ? this has to be in in just over 24 hrs ......help! Answered by Chris Fisher. 





Gray siding and stone chimneys 
20120422 

From lupita: Fifty houses are on the north side of a river. The 2nd house has gray siding, and every 5th house after that also has gray siding. The 11th house has a stone chimney; every 3rd house after that also has a stone chimney. How many of the 50 houses have stone chimneys but do not have gray siding? Answered by Penny Nom. 





What was the class average? 
20120420 

From olwale: a class which consist of 15 boys and 10 girls sit for a test. the average score of the boys is 20 and the girls' is 25. find the average score of the class. Answered by Penny Nom. 





5 machine make 5 gadgets in 5 minutes 
20120420 

From Charles: 5 machine make 5 gadgets in 5 minutes,
so how long does it take for 100 machines make 100 gadgets? Answered by Penny Nom. 





A maximization problem 
20120409 

From Nancy: After an injection, the concentration of drug in a muscle varies according to a function of time, f(t). Suppose that t is measured in hours and f(t)=e^0.02t  e^0.42t. Determine the time when the maximum concentration of drug occurs. Answered by Penny Nom. 





Water is flowing from tank A to tank B 
20120406 

From Noel: At First, Tank A was completely filled with water. The tap from Tank A was then turned on and water flowed out at a constant rate. The water which flowed out was collected into Tank B. At the end of 6 minutes, Tank A was 2/3 full. After a further 8 minutes, Tank A had 2.4 liters of water left while Tank B was completely filled with water. Find the capacity of Tank B. Answered by Penny Nom. 





A 12 foot long board 
20120405 

From Lesley: If I have a board 12 feet long and am building shelves 2 1/4 feet in
length, how many inches are left? Answered by Jaymi Peterson and Penny Nom. 





A steamroller with a 3 foot diameter and a 6 foot width makes 20 revolutions 
20120321 

From Robert: A steamroller with a 3 foot diameter and a 6 foot width makes 20 revolutions. How much ground area does it pave? Answered by Penny Nom. 





Remainders 
20120318 

From Leslie: Question: Janice has some marbles. When she divides them into groups of 4, she has 2 marbles left over. If she divides them into groups of 5, she will also have 2 left over. What is the least number of marbles she can have? Answered by Penny Nom. 





Buying school supplies 
20120309 

From Jada: Hi, my daughter is having difficulties with a problem she is in the 5th grade, and insisted that it was a guess and check problem, but she really doesn't understand, and I don't either. Can you help us out?
Danielle is buying school supplies. She
has $7.25 to spend.
Notebook: $0.75
Pencils: $1.95
Pens: $2.50
Planner: $5.00
Please help by explaining the guess and check strategy for a problem like this. Thank you. Answered by Penny Nom. 





A clock takes 3 seconds to strick the hour of 3 o'clock 
20120309 

From saptarshi: [ A clock takes 3 seconds to strick the hour of 3 o'clock. How many seconds will it take to strick 9 o'clock?] Answered by Robert Dawson. 





Tina is older than Catherine by 1 year and 7 months 
20120303 

From jennifer: Tina is older than Catherine by 1 year and 7 months. Karen is
younger than Tina by 2 years and 11 months. If Karen is 7 years and
2 months old, find out Catherine's age. Answered by Penny Nom. 





Mr. Schneider's mass 
20120229 

From Khiya: Mr. Schneider's mass is 2 digits. The first digit is 3 times the second digit. Both digits are odd numbers, and his mass is greater than 35 kg. What is Mr. Schneider's mass? Answered by Penny Nom. 





The 10000th day of her life 
20120221 

From derrick: Ella was born early in the morning on a Friday.She got married on the 10000th day of her life. What day of the week was it? Answered by Penny Nom. 





Tim sells 6 times as many oranges as apples 
20120220 

From Bronwen: Tim sells 6 times as many oranges as apples. If he sell 490 in total one morning, how many of each type were sold? Answered by Penny Nom. 





Demarkus is paving a new driveway 
20120219 

From Anita: Demarkus is paving a new driveway for a local YMCA volunteer club. The driveway is 90 yards long and 6 yards wide. If the concrete cost $2.50 per square foot, how much will it cost Demarkus to cover the driveway? Answered by Penny Nom. 





Margie threw a ball 
20120216 

From mary: at 9:45 Margie threw a ball upwards while standing on a platform 35ft above the ground. The height after t seconds follows the equation:
h(t)= 0.6t^2 +72t+35
a) what will be the maximum height of the ball?
b)how long will it take the ball reach its maximum height?? Answered by Harley Weston. 





Figures with dots 
20120215 

From A: Okay so my daughter came home and had this question for homework from her teacher. I have no idea what it means HELP!!
The question shows a figure that is a square. It has 5 dots on the top, bottom and on the sides looks similar to this:
. . . . .
. .
. .
. .
. . . . .
they want to know 3 more ways to show the number of dots in the figure. They have already shown one with just counting them
and the other one that they showed was circling the four corner dots and then taking the dots in between with a number sentence set up
like this: 4+4*(52) = 4+4*3= 16. They also besides giving 3 ways want us to write a number sentence and an algebraic sentence to show the number of
dots in the figure with "n" sides. Please help! So confusing ! I don't know if my square turned out or not but it should be 5 across the top and bottom and
on the sides and no dots in teh middle it is just the outside. Answered by Penny Nom. 





A word problem 
20120215 

From Bo: Jane guessed a number. Tom guessed a number that was double the sum of 1 more than twice the number guessed by Jane. Sum of the numbers guessed by both were 27, what are the numbers? Answered by Penny Nom. 





A 3 to 1 ratio of girls to boys 
20120212 

From amanda: At a recent school dance it was observed that there was a 3 to 1 ratio of girls to boys. If 204 students attended the dance, how many boys, and how many girls were there? Answered by Penny Nom. 





A two digit number 
20120129 

From Christine: Five times the sum of the digits of a two digit number equals the number. If the digits are reversed, it becomes nine more than the original number. What is the original number?
I really don't understand this question, help me please Answered by Penny Nom. 





Today is Emma's Birthday. 
20120125 

From Mike: Today is Emma's Birthday.
Emma's mother is four times as old as Emma is today.
In four years, Emma's mother will be three times as old as Emma.
How old is Emma today? Answered by Penny Nom. 





Four pizzas 
20120123 

From kris: a pizza company wishes to put 4 medium pizzas in a box to sell as a party pack. The box they want to use the square and has dimensions of 60cm by 60cm. They need you to help them calculate the dimensions of the pizza that will fit in the box. Calculate the following: area, radius, diameter, circumference Answered by Penny Nom. 





A problem in logic 
20120119 

From Ghader: The puzzle below I know the answer to; because someone told me! My question is: how could I answer it using logic, maths, etc. what field of inquiry does this kind of problem fall into?
Puzzle: You are in a room with two men: one is a compulsive liar and the other is a compulsive honest. There are two doors: one leading to heaven, the other to hell. The two men know which door leads to where. You want to go to heaven but are allowed only ONE question from one or the other of the two men. What would that question be?
[The question to ask, from either man, is: "if I asked the OTHER man which door leads to heaven, which door would he point?". You would then choose the other door.]
Has this answer got any basis in logic or maths at all? Answered by Robert Dawson. 





Four apples and two oranges cost Rs. 30... 
20120113 

From nasr: Four apples and two oranges cost Rs. 30, and one apple and 3 oranges costs Rs.15.How much does each apple and each oranges cost? Answered by Harley Weston. 





A picture in a frame 
20120110 

From nnadozie: a picture, which measures 46cm by 38cm, is surrounded by a frame, which is 2cm wide, find the area of the frame. Answered by Penny Nom. 





Designing aluminum cans 
20120108 

From swathi: A company manufactures aluminum cans. one customer places an order for cans that must be 15 cm high, with a volume of 1200cm cube.
a) use the formula V= pie r squared h to determine the radius that the company should use to manufacture these cans
b) graph the function that corresponds to 0 = pie r squared h minus V to determine the radius. Answered by Penny Nom. 





A wire spiral 
20120107 

From Pinar: I am trying to help my daughter with very challenging maths questions which sometimes I get stuck
If someone help me with one of them I would appreciate it.
Jane is making a spiral out of wire. She bends the wire after 1 cm, then bends the wire
after 2cm, then 3cm and continues in this manner. After 4 bends she used 15 cm of wire
For each bend how many cm wire was used? After 6 bends how many cm wire will she have used?
How many bends will she have made if she uses 66 cm of wire?
I would appreciate if somebody would help me with this.
Thank you!
Pinar Answered by Penny Nom. 





Two trains passing each other 
20111207 

From Tamkeen: two trains 245m and 315m long are travelling toward each other at 90km/h and 54km/h respectively on parallel lines . how long do the train take to pass one another train the time they meet each other? Answered by Penny Nom. 





Squares and triangles 
20111206 

From Liaqath: You have squares and triangles.
Altogether there are 33 sides.
How many squares do you have?
How many triangles do you have? Answered by Penny Nom. 





What is the altitude of the balloon? 
20111204 

From C: Chelcy and Jorgeare 2.32 miles apart. The observe a hot air balloon directly overhead between them Chelcy's angle of elevation is 28 degrees. Jorge's Angle of elevation is 37 degrees. What is the altitude of the balloon? Answered by Penny Nom. 





A suspension bridge 
20111130 

From jennifer: suspension bridges like the golden gate bridge, are used to span large distances.
when the main curved cables are attached to the deck by vertical cables they will end
up in the shape of parabola. assume that we need to build a bridge that spans
2,400 feet. the two towers 165feet tall each where placed at 400feet from either
side. the lowest point of the center of the bridge at 10feet. vertical suspension cables
where placed at 25foot interval. how many feet of cable are needed to connect
the deck to the main cables between the two towers? show all working. Answered by Penny Nom. 





Four carpenters can build eight houses in 10 days. 
20111123 

From Kenneth: Four carpenters can build eight houses in 10 days.
Two carpenters can build how many houses in 15 days? Answered by Penny Nom. 





The dimensions of a rectangle 
20111111 

From Ivan: The length of a rectangle is 31 centimeters less than five times its width. Its area is 72 sq centimeters. Find the dimensions of the rectangle. Answered by Penny Nom. 





3 fish 
20111027 

From Ann: You have 3 fish weighing a total of 21 lbs. The largest fish weighs twice as much as the second fish and the third fish weighs half the amount of the second fish.
So how much does the third fish weigh? Answered by Penny Nom. 





The end of a swimming pool 
20111017 

From Jim: "The end of a swimming pool is a rectangle inclined 45° to the horizontal.
The edge at the surface is 12 feet long and the submerged edge is 10 feet long.
Could you draw a diagram for me ? I don't understand the Problem. Answered by Penny Nom. 





One central circle and three tangent circles 
20111016 

From Margaret: You have one central circle and three or more circles tangent to the outside of the circle of varying radii. You know the x,y coordinates of the centers of the other circles. If you now remove that central circle (and pretend you never knew where it was), can you calculate its center in x,y coordinates? Answered by Chris Fisher. 





Expanding the size of a table 
20111016 

From Ericka: You are working as a carpenter in an industrial Shop. A customer came to you and inquired about the size of the table which would be fitted in her room. She informed you that she had already a 1.5 x 1m table in her room but she wanted to maximize the space by adding the same amount to is length and width. She is planning to occupy a 3 square meter place on her room for her to work comfortably. She is requesting you a written recommendation before she asked to make a table. What amount should be added to both sides to maximize a 3 square meter area? Answered by Penny Nom. 





Twice an even number 
20111010 

From Ron: The number of dollars that Tracy has in her pocket is an odd number.
Hal gave Tracy $2 more than she already had in her pocket.
The number of dollars Tracy now has cannot be _________.
a) $60 b) $62 c) $64 d) 68 Answered by Penny Nom. 





What is the speed of the boat in still water? 
20111007 

From Hannah: The speed of a stream is 3 mph. A boat travels 10 miles upstream in the same time it takes to travel 16 miles downstream. What is the speed of the boat in still water Answered by Penny Nom. 





Three consecutive odd integers 
20111007 

From Muneera: Find 3 consecutive odd integers so that 3 times their sum is 5 more than 8 times the middle one? Answered by Penny Nom. 





Linear equations 
20111006 

From Hannah: I am confused about a question on my homework, here is an example on what I need to do:
You own a sightseeing boat tour. Kids' admission costs $5, adults' admission costs $8.
During that day you get (madeup number) $521 with 71 admissions.
How many of each passenger boarded?
I tried something like
5x + 8y = 521
x + y = 71
But, I still don't understand how to solve it! Help? Answered by Penny Nom. 





Three men sharing a task 
20110927 

From Olaniyan: Three men do a piece of work, the first does 7/15, the second does 5/6 of the remainder while the third does the rest.if the rest done by the third person equals 24 units, find the whole piece of work? Answered by Penny Nom. 





90 cm of pipe 
20110926 

From margie: A 90cm pipe is cut into two pieces so that one pieces is 6cm shorter than the other. how long was each piece? Answered by Penny Nom. 





A tank is 3/8 full 
20110924 

From Olaniyan: When 150 liters has been drawn from a tank, it is 3/8 full; how many liters will the tank hold? Answered by Penny Nom. 





5 crayons 
20110917 

From John: How many four color combinations are possible with 5 crayons Answered by Penny Nom. 





A rectangle of largest possible area 
20110916 

From mary: Steven has 100 feet of fencing and wants to build a fence in a shape of a rectangle to enclose the largest possible area what should be the dimensions of the rectangle Answered by Penny Nom. 





A rectangular wall 
20110912 

From Jimi: The area of a rectangular wall of a barn is 110 square feet. It's length is 12 feet longer than twice its width. Find the length and width of the wall of the barn. Answered by Penny Nom. 





The cost of petrol 
20110826 

From Sam: Hi, i'm confused about this question from my textbook, here goes:
The cost of petrol for a 240 km journey for a car which runs 12 km on
each litre of petrol is $24. What would be the cost of petrol for a 500
km journey for a van which runs 11km on each litre of petrol?
please answer in detail and thanks in advance :) Answered by Penny Nom. 





A picture with a frame 
20110819 

From Aniish: A picture 8inches by 12inches is placed in a frame of uniform width. If the area of the frame equals the area of the picture find the width of the frame? Answered by Penny Nom. 





Fencing around a pool 
20110712 

From Anita: The measurement of a swimming pool are 32 feet by 18 feet. How much fencing is needed if the fence is to be built 7 feet from each side of the pool? Answered by Penny Nom. 





concentric circles 
20110706 

From maribiie: two circles are concentric. the tangent to the inner circle forms a chord of 12cm in the larger circle. find the area of the "ring" between the two circles? Answered by Penny Nom. 





How tall is the pole? 
20110527 

From cynthia: 20 foot rope is tied 2 feet from the top of a pole and secured 8 feet from the base of the pole....How tall is the pole? Answered by Penny Nom. 





How many meters long should the race be? 
20110526 

From Lee: Nathan can walk at a rate of two meters per second while David can
easily go threeandahalf meters per second. David offers Nathan
a 45 meter head start. How many meters long should the race be in
order for Nathan to win by a nose Answered by Penny Nom. 





Problem solving with fractions 
20110521 

From emilyd: I had a packet of sweets. I put 1/5 of the sweets into Container A, 1/3 of them in Container G, 10 sweets in container C and the rest in container D. If the number of sweets in container D is equal to 75% of the total number of sweets in container A and B, how many sweets are there altogether? Answered by Penny Nom. 





What was his salary before the raise? 
20110516 

From Annette: Need to show all my work and round to the nearest dollar.
If James received a 9% raise and is now making $102.00 per year, what was his salary before the raise? Answered by Penny Nom. 





The dimensions of a rectangle 
20110508 

From yolanda: If the length of a rectangle is 3ft less than twice its width and the area of the rectangle is 54ft^2,what are the dimensions of the rectangle? Answered by Penny Nom. 





How many students are 25 and under? 
20110501 

From ella: use the five steps of problem solving to answer the following question
Enrollment at a local university is 8,500. There are one third as many students over the age of25. there are 25 and under. how many students are 25 and under and how many are 25 and older(p 5) Answered by Penny Nom. 





The area of a rectangle 
20110430 

From Hayley: A rectangles width is exactly twice its length. The area of the rectangle is 450 square feet. What are the length
and width of the rectangle? Answered by Penny Nom. 





Deciding where to bowl 
20110429 

From ella: the bowling alley on wedge street charges $5.50 for shoe rentals plus $2.50 per game. lawerence bowing alley charges $4.00 shoe rentals and $3.00 per game . how many games should they bowl to make wedge street cheaper than lawerence street Answered by Penny Nom. 





Dividing the profits 
20110419 

From Tracy: I need to know how to come up with the answers to the following problems. I need to be able to show my work. So can you help me on how to come up with the answers to questions like these. Thanks.
Three individuals form a partnership and agree to divide the profits equally. X invests
$9,000, Y invests $7,000, Z invests $4,000. If the profits are $4,800, how much less
does x receive compared to having the profits divided in proportion to the amounts
invested by X, Y, and Z?
In printing an article of 48,000 words, a printer decides to use two sizes of type. Using the
larger type, a printed page contains 1,800 words. Using a smaller type, a page contains
2,400 words. The article is allotted 21 full pages in a magazine. How many pages must be
in smaller type? ___________
thank you Answered by Penny Nom. 





Ramon has 6 puppies 
20110417 

From Mary: Ramon has 6 puppies. Five of the 6 weigh the same and one puppy is heavier. If Ramon had a balance scale, what is the least number of times he could weigh the puppies to be sure he could determine which puppy was heavier? Answered by Penny Nom. 





Cone story problem 
20110416 

From Chelsea: There is a cone with a story problem that states only that the radius is the same as the altitude and that the slant height of the cone is 6cm. I have no idea how to figure this problem out. Answered by Penny Nom. 





Decreasing numbers 
20110413 

From Hadi: A number is called a "decreasing number" if each digit in the number is less than the digit to its left.
For example, 87420 is a deceasing number. How many fivedigit
decreasing numbers are there? Answered by Claude Tardif. 





The perimeter of a rectangle 
20110404 

From aspen: the perimeter of a rectangle is twice the sum of its length and its width. the perimeter is 40 meters and its length is 2 meters more then twice its width. what is the length? Answered by Penny Nom. 





If 25 items are evenly spread over 7 days 
20110323 

From michael: What is the formula to calculate:
If 25 items are evenly spread over 7 days, but one day has 3 items less than the other days, what is the number if items for each of the remaining 6 days? Answered by Penny Nom. 





Find his income on the fourth week of August. 
20110322 

From Abeth: The average weekly income of MJ for the first three weeks of August was 3,600 and his average weekly income for four weeks is 3950. Find his income on the fourth week of August. Answered by Penny Nom. 





Tony and his friends 
20110321 

From Mieke: Using the following statements and the information given, how much money did each friend have.
Mike says, "I have $41.00 more than Tony."
Jessica says, "I have 6 times as much as Tony plus $2.00."
Ashley says, "I have 13 times the amount Tony has."
Sara says, "I have the 8 times the amount Tony has."
The total together they had was $304.00 Answered by Penny Nom. 





A verbal problem 
20110320 

From tom: mrs. jhonson planned to spend $78 for fabric to make draperies. She
found her fabric on sale at 20% less per yard than she expected and was
able to buy her drapery fabric plus 4 extra yards for bedspread for $83.20. how much fabric had she planned to buy and what was the original cost per yard? Answered by Stephen La Rocque. 





How much per ft. does it cost? 
20110314 

From Linda: 350 lbs. of coil at $1.80 per lb equals $630. each coil is 780 ft. how much per ft. does it cost? Answered by Penny Nom. 





A two digit number 
20110301 

From jhoanna: the sum of the digits of a two digit number is 10. The value of the number is 16 times the units digit.Find the number. Answered by Penny Nom. 





Find the dimension of the original rectangle 
20110228 

From sandra: the perimeter of a rectangle is 40 cm. if the length were doubled and the width halved, the perimeter would be increased by 16cm. Find the dimension of the original rectangle Answered by Robert Dawson. 





A word problem 
20110226 

From Barb: there are five times as many children as adult at a playground. There
are 60 people on the playground.
write an algebra equation that represents this situation. Be sure to define
your variables.(start with statement "Let X= ___") Answered by Penny Nom. 





Tom has 12 times as much money as Bill 
20110218 

From Chris: Tom has 12 times as much money than Bill. Together they have $325 dollars. How much does each boy have? Answered by Stephen La Rocque. 





Two conical tanks 
20110217 

From rustom: Two vertical conical tanks (both inverted) have their vertices connected by a short horizontal pipe.
One tank, initially full of water, has an altitude of 6 ft. and a diameter of base 7 ft.
The other tank, initially empty, has an altitude of 9 ft., and a diameter of base 8 ft.
If the water is allowed to flow through the connecting pipe, find the level to which
the water will ultimately rise in the empty tank (Neglect the water in the pipe.) Answered by Penny Nom. 





(11/2)(22/3)(33/4)...(1515/16)=n!/16 
20110215 

From Fiona: Could you help me find the value of n: (11/2)(22/3)(33/4)...(1515/16)=n!/16 Answered by Penny Nom. 





What is the 6001st digit that Sam wrote? 
20110215 

From Sarah: Sam wrote the natural numbers from 1 to 5280 in order. What is the 6001st digit that Sam wrote? Answered by Penny Nom. 





Throwing a football 
20110208 

From Janet: a football is thrown into the air from 2 meters high. After 1 second it is 6.9 meters high. After another second it is 2 meters high. How high is it after 1.02 seconds and .05 seconds? when will it reach 5.136 meters? I am not sure how to extract the numbers I need and what equations to use them in? Answered by Stephen La Rocque. 





Reversing the digits 
20110208 

From rejie: if the digits are reverse , the number is 9 less than the original number.what is the equation? Answered by Penny Nom. 





An even multiple of 27 
20110201 

From parth: the 6 digit # 63x904 is an even multiple of 27 what is X Answered by Penny Nom. 





The area of a rectangle 
20110131 

From T.S.: for which value of w does the rectangle below have an area of 864 square units if sides are width=w+15 and length=w15 Answered by Penny Nom. 





A rectangle 
20110116 

From meg: if a rectangle has a length that is 3cm less than 4 times its width and its perimeter is 19cm, what are the dimension? Answered by Penny Nom. 





Matt is thinking of two numbers 
20110114 

From mary: Matt is thinking of two numbers. One number is 9 more than the other number. The sum of the numbers is 45. What are the numbers? Answered by Penny Nom. 





The height of a lamp 
20110113 

From Dorothy: I need to find the lamp height with casting shadow (base line of triangle where a boy 1.6m tall stands 3m from base of street lamp and has a 2m shadow. In other words, think of a right angle triangle with zero height starting at left, then 2m to right stands boy (1.6m high). Angle (hypotenuse) increases up to top of street lamp with 'x' height and 3m base. Answered by Penny Nom. 





The weight of a tank 
20110111 

From tom: A tank, open at the top is made up of thin sheet iron 1in. thick. The internal
dimensions of the tank are 4 ft. 8in. in long ;3 ft. 6 in.in wide ;4ft 4 in. in deep
Find the weight of the tank when empty, and find the weight when full of salt
water. (Salt water weighs 64 lbs. per cu. ft., and iron is 7.2 times as heavy as
salt water) Answered by Harley Weston. 





Draw a figure with 16 triangles using only 6 line segements 
20101216 

From Jill: How can you draw a figure with 16 triangles using only 6 line segements? Answered by Stephen La Rocque. 





The length is twice its breadth 
20101209 

From jenu: The length of the rectangular field is twice its breadth. A man jogged around it 5 times and covered a distance of 3 km. what is the length of the field? Answered by Penny Nom. 





Fifty votes were cast in a class election 
20101203 

From nympha: Fifty votes were cast in class election, Beth got 1/5 of the votes. Helen got as many votes as Jane and Peter put it together. Peter got 1/3 as much votes as Jane. How much votes did each of the four candidates received? Answered by Stephen La Rocque. 





How many gallons of water will it take to fill a classroom? 
20101201 

From deena: How many gallons of water will it take to fill a classroom that is 26 feet long by 19 feet wide and 9 feet high? How many tons of water will that be? Answered by Stephen La Rocque. 





A rectangular piece of plywood 
20101130 

From Austin: A rectangular piece of plywood is trimmed to make it square by cutting a 4cm strip off the top and a 2cm strip off one side. If the area of the original piece is 74cm2 greater than the area of the square, find the dimensions of the rectangle. Answered by Penny Nom. 





Two girls agree to mow a lawn 
20101123 

From Milorad: Two girls agree to mow a lawn 60m by 80m so that the first girl cuts one half by
cutting a uniform strip around the lawn. How wide a strip should the first girl cut?
I've been struggling with the question above, mainly with the equation and I have
set it up as 2400=(602x)(802x), if this is incorrect I would like to know where I've
gone wrong and also would like a full answer to see it properly done. I need an algebraic
answer and not one with a diagram. Answered by Penny Nom. 





Will the ball clear the tree? 
20101114 

From MK: Sam hits a golf ball with a fiveiron a distance of 120m horizontally. A tree 45m high and 35m in front of Sam is directly in the path of the ball. Will the ball clear the tree if the ball makes a parabolic curve and has a maximum height or 80m? Answered by Brennan Yaremko. 





Three consecutive odd integers 
20101107 

From karen: find three consecutive odd integers such that twice the sum of the second and the third is 43 more that three times the first Answered by Penny Nom. 





Nickels as dimes 
20101106 

From Exie: Clara has the same number of nickels as dimes in each jar. there are 15 cent in one jar and 30 cents in the other. how many of each coin does she have in each jar?
I'm home schooling my granddaughter and this problem has me stumped..could you please help? thanks Answered by Robert Dawson. 





Bbippities, bops, and boos 
20101105 

From Stacey: six bippities equal three bops,and six bops equal two boos. How many
boos are there in one bippity,one bop, and one boo?? Answered by Stephen La Rocque. 





Nickels and dimes 
20101105 

From kebede: John has 20 fewer nickels than dimes. The total of the nickels and dimes if $12.35. ow many of each coin does she have? Answered by Penny Nom. 





Four tires and a spare 
20101104 

From stacey: a car is driven 40,000 miles using four tires and a spare. the tires are
rotated so that each tire travels the same number of miles. What is the
number of miles traveled by each tire??
HINT: the answer is not 8,000 miles each.. Answered by Penny Nom. 





A box full of oranges 
20101028 

From Mary: A box full of oranges weighs 9 pounds. After a family ate 2/3 of the oranges, the remaining oranges and the box weighed 4 pounds. The weight of the box when empty is how many pounds? Answered by Penny Nom. 





Electronic cars around a circular track 
20101011 

From Taylor: Cory and Melissa are racing electronic cars around a circular track. They begin at the same time going in the same direction. Cory's car completes a revolution in 35 secs, while Melissa's car completes a revolution in 30 secs. How long will it take them before both cars reach the starting point again simultaneously? Answered by Stephen La Rocque and Penny Nom. 





Two numbers 
20100914 

From Sania: math homework helpFelicia is thinking of two numbers. One of them is 2 more than 3 times the other one. The difference between the squares of these numbers is 112. What is the smaller number? Answered by Penny Nom. 





Choose any three digits that are less than ten 
20100912 

From cecille: my son have a homework, but i don't understand the question. here's the problem:
choose any three digits that are less than ten.
make all the two digit number you can using those three digits.
add up the two digit numbers you created and divided by the
sum of the original three digits.
record your answer. then do it again with another three digits. write your observation about
the answer. Answered by Claude Tardif. 





Mrs. Johns graded 121 math tests. 
20100910 

From Tums: Mrs. Johns graded 121 math tests. It took her 3 hours to grade all of the tests. Each test took the same amount of time to grade. About how many test did Mrs. Johns grade in 2 hours? Answered by Penny Nom. 





A truck goes south and then east 
20100826 

From MARK: A truck starts at point A and drives South 3 miles. Then it turns left at Point B and drives east four miles to point C. How many miles is the truck at point C from point A if it were to drive directly from point A to Point C.My book says the answer is 5 miles. How did they come up with the answer? Answered by Robert Dawson. 





12 coins 
20100707 

From Eden: We have 12 coins same in size and shape and also weight.
But among these, one coin which has same size and shape, but not in weight
and we can't know that this coin was lighter or heavier.
We must decide which coin was lighter or heavier among these 12 coins in
4 times of weighting with scale. Answered by Stephen La Rocque and Tyler Wood. 





A collection of baseball cards 
20100701 

From Martha: Cody has a collection of baseball cards. Is it possible for him to
place the cards into 5 boxes so that exactly 3 of the boxes contain an
odd number of cards and the total number of cards in two of the boxes
is the same as the total number in the other 3 boxes? Explain. Answered by Robert Dawson, Penny Nom and Claude Tardif. 





The product of 2 consecutive integers 
20100628 

From Sharon: the product of 2 consecutive integers is 6 less than the square of the larger number.
find the smaller number Answered by Penny Nom. 





Roosters, hens and chicks 
20100610 

From Kamarah: If a rooster is worth 5 coins and a hen is worth 3 coins and chicks 3 together are worth 1 coin, how many roosters, hen and chicks totaling 100 can be bought with 100 coins?
notes:
you must buy at least one of each type of fowl
no fractional fowl
chicks are purchased in multiple of 3
find 3 solutions Answered by Penny Nom. 





The tires on Helen's new car 
20100608 

From Rich: Helen bought a new car with four tires and a fullsize spare. If she rotated the tires so that each tire would have the same amount of wear, then how many miles were on each tire when her odometer showed 40,000 miles? Answered by Penny Nom. 





Going to the bike shop 
20100607 

From Omi: Marie rode her bicycle from her home to the bicycle shop in town and then walked back home. If she averaged 6 miles per hour riding and 3 miles per hour walking, how far is it from her home to the bicycle shop if her total travel time was 1 hour? Answered by Penny Nom. 





Two problems 
20100527 

From debbie:
Question from debbie, a parent:
hi, i have a daughter and she asked me a maths question I cannot solve. I was just wondering if you can give me the answers plus the working out so I could explain to my daughter,
1. The leftmost digit of a sixdigit number N is 1. If this digit is removed and then written as a rightmost digit, the number thus obtained is three times N .Find N.
2. Four friends are racing together down a flight of stairs. A goes 2 steps at a time, B 3 steps at a time. C 4 steps at a time and D 5 steps at a time. The only steps which all four tread on are the top one and the bottom one. How many stairs in the flight were stepped on exactly once? Answered by Penny Nom. 





What is the speed of the current? 
20100525 

From tien: a boat travels upstream, against a current, at a speed of 4 miles per hour. On the return trip, the boat travels downstream, with the current , at 10 miles per hour. the speed of the current remains constant. what is the speed of the current? Answered by Penny Nom. 





How wide a strip has he cut when the lawn is half mowed? 
20100524 

From Arib: rectangular lawn has length 40 m and width 30 m. David starts cutting from the outside in. How wide a strip has he cut when the lawn is half mowed? Answered by Penny Nom. 





What is the distance from A to C via B? 
20100524 

From vivianne: The distance from A to B is d km and that from B to C is x km. if a bus maintains an average speed of 50km/hr between A and B and 60km/hr between B and C, it takes 3 hours to travel from A to C. If it maintains 60km/hr between A and B and 50km/hr between B and C, the journey takes 8 minutes less. What is the distance from A to C via B? Answered by Penny Nom. 





An optimization problem 
20100523 

From Marina: Hello, I have an optimization homework assignment and this question has me stumped..I don't even know A hiker finds herself in a forest 2 km from a long straight road. She wants to walk to her cabin 10 km away and also 2 km from the road. She can walk 8km/hr on the road but only 3km/hr in the forest. She decides to walk thru the forest to the road, along the road, and again thru the forest to her cabin. What angle theta would minimize the total time required for her to reach her cabin?
I'll do my best to copy the diagram here:
10km
Hiker_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _Cabin
\  /
\  /
f \ 2km /
\  /
theta \___________________________ /
Road Answered by Penny Nom. 





How far is the runner from the starting point? 
20100522 

From Richard: A marathon runner runs 6 miles south and then 8 miles east. How far is the runner from the starting point? Answered by Tyler Wood. 





How far am I from the starting point? 
20100518 

From jilayna: if i walk 5 miles north, 7 miles east, and 3 miles north again.to the nearest tenth of a mile ,how far,in a straight line, am i from my starting point Answered by Penny Nom. 





The sum of twice a number and 6 is 8 
20100512 

From MAE: THE SUM OF TWICE A NUMBER AND 6 IS 8 . FIND THE NUMBER Answered by Penny Nom. 





The product of two consecutive even integers 
20100511 

From Terry: The product of two consecutive even integers is 14 more than their sum. Find the integers. Answered by Penny Nom. 





The dimensions of a driveway 
20100507 

From Josh: Dave and Jane have a new rectangular driveway. The perimeter of the driveway is 168 feet. The length is 12 feet longer than three times the width. What are the dimensions of the driveway? Answered by Penny Nom. 





The width of a picture frame 
20100428 

From Daniel: The frame of a picture is 28 cm by 32 cm outside and is of uniform
width. What is the width of the frame if 200 cm ^2 shows? Answered by Penny Nom. 





A rectangular laundry room 
20100428 

From Cynthia: a laundry room is shaped like a rectangle. the area of the room is 6 square yards. the perimeter is 10 yards. The room is longer than it is wide. How wide is the room? How long it the room? Answered by Penny Nom. 





A rectangular prism 
20100427 

From Savannah: A rectangular prism is made of exactly 8 cubes. Find
the length, width, and height. Answered by Penny Nom. 





A rectangular garden 
20100425 

From Billy: Tanisha wants to make a rectangular garden with a perimeter of 38 feet. What is the greatest area possible that tanisha can make the garden? Answered by Penny Nom. 





A table of values 
20100422 

From Donna: Complete the table by determining the value of each letter. Explain what rule is used to relate the numbers in the second column (with the heading of y) with those in the first column (with the heading of x).
x  y
3  5
9  23
4  8
6  A
7  B
C  11
D  2
I can't figure this out, can you help me? Answered by Robert Dawson. 





The length and width of a table 
20100419 

From Linda: The length of the top of a table is 2 feet longer than 4 times the width.
The area is 72m squared. Find the dimensions of the table. Answered by Penny Nom. 





What are the dimensions of the box? 
20100413 

From Steven: The longest rod that will just fit inside a rectangular box,
if placed diagonally top to bottom, is 17 inches.
The box is 1 inch shorter and 3 inches longer than it is wide.
How much must you cut off the rod so that it will lie flat in the
bottom of the container? What are the dimensions of the box? Answered by Robert Dawson. 





A rectangle problem 
20100412 

From Charlene: The ratio of the width to the length of a certain rectangle is equal to the ratio of its length to the difference between its length and twice its width. If the area of the rectangle is 25cm^2, then what are its dimensions? Present a non algebraic solution? Answered by Tyler Wood. 





The perimeter of a rectangle 
20100412 

From Charlene: The area of a rectangle is 390m^2. If its length is increased by 10m and its width is decreased by 6m, then its area does not change. Find the perimeter of the original rectangle. Answered by Tyler Wood. 





A cube with twice the volume 
20100411 

From Woojin: From a given cube create another cube with twice the volume.
the cube: 5cm each. Answered by Tyler Wood. 





Working backwards 
20100411 

From adel: alice gave reggie and freddie as much money as each had already.reggie in turn gave alice and friddie as much money as each already had in negotiable treasury notes. freddie gave alice and reggie as much money as they each had. in the end they each had the same sum, 24000.00.how much money did they each in the beginning? Answered by Penny Nom. 





A max min problem 
20100406 

From Terry: The vertex of a right circular cone and the circular edge of its base lie on the surface of a sphere with a radius of 2m. Find the dimensions of the cone of maximum volume that can be inscribed in the sphere. Answered by Harley Weston. 





A ratios problem 
20100401 

From Jules: 1a) If 2/3 of the boys and 3/4 of the girls at a party are dancing, what is the
ratio of boys to girls, if all the dancing couples consist of a boy
and girl?
b) If the total number of the boys and girls of the party is 153, how
many boys are at the party? Answered by Penny Nom. 





Coins in 3 parking meters 
20100327 

From Zena: There are 227 coins altogether in 3 parking meters.
The second meter has 37 more coins than the first meter.
The third meter has twice as many coins as the second.
How many coins in each meter? Answered by Penny Nom. 





A ladder against a wall 
20100325 

From amber: the distance from the bottom of the ladder to the building is18 foot less than the length of the ladder.How high up the building is the top of the ladder if that distance is 1 ft less than the length of the ladder? Answered by Penny Nom. 





What is the speed of the current? 
20100317 

From Carl: If you can row 3 mph in still water and paddle 3 miles upstream and return in 3.6 hours then what is the speed of the current? Answered by Penny Nom. 





Gina's weight was 4/7 of Helen's weight 
20100314 

From Eileen: At first, Gina's weight was 4/7 of Helen's weight. Then, Gina gained 3kg while Helen lost 6kg. They are the same weight now. What is Helen's weight now? Answered by Penny Nom. 





A red boat and a blue boat 
20100313 

From SERENA: Two fishing boats set out at 2pm for some afternoon fishing. Both boats pulled out from the same dock heading in the same direction. The average speed of the blue boat is 30mph slower then twice the speed of the red boat. In two hours, the blue boat is 20 miles ahead of the red boat. Find the rate of the blue boat. Answered by Penny Nom. 





Selling lettuce 
20100311 

From Mike: Day 1 started with 80 heads of lettuce and x were sold.
Day 2 started with two times the number of heads of lettuce that was left
over. Again, only x were sold. Day 3 started with 3 times the number
of lettuce from what was left over from day 2 and all was sold. What
was the # of lettuce sold on each day? Answered by Penny Nom. 





Redwood Park and Glendale Park 
20100305 

From Shaun: Question from Shaun, a student:
Redwood and Glendale Parks are each surrounded by 100 yards of
fencing. The are of Redwood Park is 25 square yards more than the area
of Glendale Park. If both parks are rectangles, what is the measurement
of each rectangle? Answered by Harley Weston. 





How many people in total came to the museum that day? 
20100305 

From simon: 1354 people attended exhibition A and 1427 people attended exhibition B. 79% of people attended both exhibitions. How many people in total came to the museum that day Answered by Penny Nom. 





The area of a new parking lot 
20100304 

From nayle: The owner of a parking lot at the beach wants to increase the parking area of the lot. If the owner increases each of the dimensions of the rectangular lot by half its original value, by what factor will the parking lot increase? Answered by Penny Nom. 





At what time would Joan catch Jo? 
20100304 

From Rusty: If Jo left his house at 6:30am traveling at 5mph and Joan left the same house 7:00am traveling at 8mph, at what time would Joan catch Jo? Answered by Penny Nom. 





The dimensions of a rectangle 
20100303 

From Kirsten: A rectangle is twice as long as it is wide. Its area is 128 square meters. What are the dimensions of the rectangle? Answered by Tyler Wood. 





Two adjacent rectangular dog pens 
20100301 

From Janet: Clint is constructing two adjacent
rectangular dog pens. Each pen will be three times as long
as it is wide, and the pens will share a common long side.
If Clint has 65 ft of fencing, what are the dimensions of
each pen? Answered by Penny Nom. 





How many CDs and videos did the store sell? 
20100301 

From dawn: A used book store started selling CDs and videos. In the first week,the store sold 40 used CDs and videos,at 4.00
per CD and 6.00 per video.The sales for both CDs and videos totaled 180.00 she wrote a system of equations to represent the situation.Then she graph the system of equations
thanks Dawn Answered by Tyler Wood. 





A mixture problem 
20100224 

From Nathan: How many gallons of 60% solution must be added to 40 gallons of a 10% solution to produce a 20% solution? Answered by Penny Nom. 





Dividing between between two charities 
20100222 

From Latoya: a 149,000 estate is to be divided between two charities so that one charity receives 18,000 less than the other. How much will each charity receive? Answered by Penny Nom. 





15 men can do a piece of work in 7 days 
20100220 

From Kenneth: If 63 books cost $126, what will 125 books cost?
If 15 men can do a piece of work in 7 days, in how many days can 21 men do the same work? Answered by Penny Nom. 





The dimensions of a flag 
20100215 

From dawn: a state flag was twice as long as it was wide and had an area of 288 sq inches, what were its, dimensions
Thanks Answered by Penny Nom. 





What time did susan go to bed? 
20100214 

From Sophia: Susan woke up at 7:42 Am to get ready for school. She slept for 10 and 1/3 hours. What time did she go to bed? Answered by Stephen La Rocque. 





Birds and cats 
20100213 

From Sophia: While visiting a pet store, you notice that there are only birds and cats in the cages. You can't help but wonder how many of each animal there is in the yard. But when you ask the store manager how many of each animal he has, he refuses to give a direct answer. He says there are 16 animal heads and 42 animal feet. How many birds and cats are there in the pet store? It said to show all your work. Explain in words how you found your answer. Tell why you took the steps you did to solve the problem. Answered by Penny Nom. 





The perimeter of a semicircle 
20100204 

From Sarah: The perimeter of a semicircle is doubled when the radius is increased by 7. Find the radius of the semicircle. Answered by Tyler Wood. 





Consecutive even integers 
20100203 

From cassandra: find 2 consecutive even integers whose sum is 34
find 3 consecutive even integers such that 3 time the middle interger is 10 more than the greatest. Answered by Tyler Wood. 





Mixing oil 
20100203 

From Andrew: A dealer wishes to produce 300 gallons of oil worth 40cents a quart. He has oil worth 36cents a quart and oil worth 52cents a quart. How many quarts of each should he mix? Answered by Penny Nom. 





A snail on an elastic band 
20100203 

From Joe: A snail starts crawling from one end along a uniformly stretched elastic band. It crawls at a rate of 1 foot per minute. The band is initially 10 feet long and is instantaneously and uniformly stretched an additional 10 feet at the end of each minute. The snail maintains his grip on the band during the instant of each stretch. At what points in time is the snail
(a) closest to the far end of the band, and
(b) farthest from the far end of the band? Answered by Robert Dawson. 





A piece of string 8 inches long is cut in two pieces 
20100202 

From Susan: If you have a piece of string 8 inches long and cut it in two pieces. Then take the pieces and forms
each into a square such that the area of each squares added together equals 2. How long are the
sides of the squares?
Susan Answered by Penny Nom. 





A decrease in travel time 
20100130 

From Mike: if a 100 mile trip averages 50 miles per hour, how much distance does one need to travel at 90 miles per hour to decrease travel time by 10% Answered by Stephen La Rocque. 





An isosceles triangle 
20100128 

From Jazzy: An isosceles triangle is a 2 congruent (equal) sides. Of the third side is three times the length of the congruent side(s), and the perimeter is 75 cm, find the length of all three sides of the triangle Answered by Penny Nom. 





What is the length of my sidewalk? 
20100127 

From Les: Name: Les
Who are you: Student
I have a sidewalk 4"thick,4ft. wide,and I have 2cubic yards of concrete. What is the length of my sidewalk? Answered by Penny Nom. 





How high up the building does the ladder reach? 
20100119 

From rosenda: A 10 meter ladder is 6 meter from the base of a building. How high up the building does the ladder reach? Answered by Robert Dawson. 





Setting up an algebraic equation 
20100118 

From jerry: the 1st of 4 books has twice as many pages as the 3rd. The 2nd book has 30 pages less than the 1st. The 4th has 42 pages more than the 1st and 2nd books combined. there are 567 pages in total. How many pages are in each book. Answered by Penny Nom. 





Gail and Bill drove to the beach 
20100110 

From Nicole: Gail and Bill drove to the beach at an average speed of 50mph. They return home over the same road at an average speed of 55mph. The tip took 30 min less time. How far is the beach from their house? Answered by Stephen La Rocque. 





Cows, pigs and ducks 
20100106 

From Eileen: There are 239 cows and pigs in a farm. The total number of cows and ducks in the farm is 767. There are 5 times as many ducks as pigs. If the farmer can sell each duck for $7.50, how much can he collect from the sale of all his ducks? Answered by Robert Dawson. 





Dividing seashells among girls 
20100106 

From Eileen: A group of girls collected some seashells from the beach. They tried to divided these seashells equally among them. If each girl received 8 seashells, they would need 5 more seashells. If each girl received 7 seashells, they would have 3 seashells extra. How many seashells did they collect from the beach altogether? Answered by Robert Dawson and Penny Nom. 





Write a function for the area in terms of x 
20100101 

From Almarie: Lauren has 40 feet of metal fencing material to fence three sides of a rectangular garden. A tall wooden fence serves as her fourth side. Write a function for the area of the garden A in terms of x, the width in feet. Answered by Penny Nom. 





The Snail Problem 
20091228 

From kishore: A snail starts crawling from one end along a uniformly stretched elastic band.
It crawls at a rate of 1 foot per minute. The band is initially 10 feet long
and is instantaneously and uniformly stretched an additional 10 feet at the end of each minute.
The snail maintains his grip on the band during the instant of each stretch. At what points in time is the snail
(a) closest to the far end of the band, and
(b) farthest from the far end of the band? Answered by Janice Cotcher. 





A ball is thrown upwards 
20091217 

From Reuben: A ball is h meters above the ground t seconds after it is thrown where
h(t) = 40t – 5t ^2 . Find the time at which the ball first reaches a height of
(a) 10 meters
(b) 40 meters
(c) 100 meters Answered by Harley Weston. 





A 4 digit number 
20091215 

From Lisa: Billy Club was assigned the task of putting numbers on
all the playground balls used during daily recess. Billy
will number the balls using the following rules:
1. It will be a 4digit number.
2. The digit in the thousands place will be a 1 or a 2.
3. The digit in the hundreds place will be a 2, 4, or 6.
4. The digit in the tens place will be an odd number.
5. The digit in the ones place will be greater than six.
How many balls can Billy number if he follows these rules? Answered by Robert Dawson. 





A telephone pole on a slope 
20091214 

From Marissa: A 10 meter telephone pole casts a 17 meter shadow directly down a slope when the angle of elevation of the sun is 42 degrees. Find the angle of elevation of the ground. Its a law of sines problem. Answered by Penny Nom. 





Two adjacent pig pens 
20091204 

From alysia: A pig farmer wants to build two adjacent pens using 96 feet of fencing. He wants rectangular pens that share the short side and the overall length is to be six more than twice the width. What should be the dimensions of the overall pen? Answered by Penny Nom. 





The dimensions of a rectangular room 
20091126 

From crystal: . The length of a rectangular room is 7 feet longer than its width. The area of the room is 60 feet. What are the dimensions of the room? Answered by Penny Nom. 





Matt has 40 coins 
20091118 

From Amy: Matt has 40 coins(nickels, dimes, and quarters). The total amount is $4.05. He has 7
more nickels than dimes. How many quarters does he have? Answered by Penny Nom. 





Two movies in one day 
20091118 

From jazzy: ann and tim saw two movies in one day.The two movies lasted 4hours long .One movie was an half hour longer than the other .How many hours did the shorter movie run Answered by Penny Nom. 





How many girls are there in the class? 
20091118 

From Anisa: There are 30 students in a class. A quarter of the boys ans half of the girls study music, making a total of 11 music students. How many girls are there in the class? Answered by Penny Nom. 





Pennies and dimes 
20091111 

From Rachel: Kesha had only pennies and dimes in her change purse. When she counted out her change she had 64 cents/ of she had 6 times as many pennies as she did dimes, how many pennies did she have? Write equation and solve it.
Can someone help me with this? Answered by Penny Nom. 





Sarah's age 
20091031 

From Kenneth: 2/3 of Mary’s age equals Sarah’s age and 3/4 of Ruth’s age equals Sarah’s age.
If the total ages equal 46, how old is each girl? Answered by Claude Tardif. 





Where is the Father? 
20091030 

From Jeffrey: A mother is 21 years older than her kid and within 6 years the child
will be 5 times younger than the mother. Where is the Father?
Jeffrey Answered by Robert Dawson and Claude Tardif. 





Sarim has $1 in coins. 
20091027 

From Elizabeth: Here is the question asked: Sarim has $1 in coins. Onefifth of the coins are dimes, twofifteenths are nickels, and twothirds are pennies. Tell how many of each coin he has. I am not sure how to start this problem. Answered by Penny Nom. 





Books on a shelf 
20091025 

From Julie: a bookshelf is 36 inches long and contains (x) books each (n) inches thick. If each book half an inch thinner, the shelf would hold six more of the same book. What is x/n Answered by Penny Nom. 





A word problem 
20091024 

From Ryan: Two times one number plus 7 times another number is equal to 17. the first number plus the second number is equal to 25. What are the two numbers? Please Help! Answered by Penny Nom. 





The three angles of a triangle 
20091013 

From Michelle: The second angle of a triangular garden is four times as large as the first.
The third angle is 45 less than the sum of the other two angles.
Find the measure of the other two angles? Answered by Penny Nom. 





What fraction of my goal has been raised? 
20091013 

From sally: If my goal is to raisel $300 and I have only raised $240 what
fraction of my goal has been raised Answered by Penny Nom. 





How many gallons does it contain when it is 1/6 full? 
20091013 

From BrenNesha: A tank contains 200 gallons when it is 4/5 full. How many gallons does it contain when it is 1/6 full? I already know the answer but i would like to know how to arrive at the answer. Answered by Penny Nom. 





A right triangle 
20091012 

From Josseph: A right triangle has an area of 84ft sq. and a hypotenuse 25ft long. What are the lengths of the other two sides? Answered by Penny Nom. 





The area of a rectangle 
20091010 

From Ann: given a rectangle with sides a and 2a and diagonal d, find the area of the rectangle as a function of the diagonal,d Answered by Penny Nom. 





$6.25 in nickels quaters and dimes 
20091010 

From miriam: a piggy bank contains $ 6.25 in nickles quaters and dimes.
there are 65 coins all together and there are four times as many nickles as quaters
find the number of coins of each kind Answered by Penny Nom. 





Two rectangles 
20091008 

From Lillian: A rectangle is 5cm longer than twice its width.
The width of another rectangle is 3cm less
than the width of the first rectangle and its length is 6cm more than 3 times its
width. If the perimeters are equal, find the dimensions of both rectangles Answered by Penny Nom. 





A dog tethered to a round building 
20090928 

From mido: One dog was linked to the outer wall of a building round of 20 meters in diameter. If the length of chain linking the dog sufficient turnover of half the distance around the building,
What area can guard dog? Answered by Harley Weston. 





Sandra's age 
20090924 

From cindy: Sandra is more than 20 years old and less than 60 years old. You can count by 7's to reach Sandra's age. Next year you will be able to count by 5's to reach Sandra's age. How old is Sandra? Answered by Penny Nom. 





24 golfers: 4 days 
20090921 

From Steven: We have 24 golfers (6 A's, 6 B's, 6 C's & 6 D's) playing 4 days.
Each day a foursome consist of an A, a B, a C & a D player.
Can you give me a pairing list so that no two golfers will play on the same foursome for the 4 days? Answered by Chris Fisher and Victoria West. 





How long would it take the students to arrive at their campsite 
20090918 

From amanda: ..."A group of 5th grade student in New Zealand are going camping. They will hike from Wellingto to Ruapehu. Then they will follow a trail for another 1/2 mile to their campsite." Ok, 1 mile equals 5,280 feet. The class decided one step length is equal to 15 inches and there are 85 steps in 1 minute. Now for the question: About how long would it take the students to arrive at their campsite, if they don't make any stops??? Answered by Robert Dawson. 





Jogging and swimming 
20090911 

From Brandon: Trevor swims jogs 3 days and swims every 4 days. How often does he jog and swim on the same day Answered by Leeanne Boehm. 





A ladder leaning against a wall 
20090908 

From Mackenzie: A 7 foot long ladder is leaning against the building. The foot of the ladder is 2 feet from the base of the building. How far up the wall is the top of the ladder? Answered by Stephen La Rocque. 





A circular border around a pool 
20090908 

From Calvin: A pool in the shape of a circle measures 10 feet across. One cubic yard of concrete is to be used to create a circular border of uniform width around the pool. If the border is to have a depth of 3 inches, how wide will the border be? ( 1 cubic yard=27 cubic feet ) Answered by Stephen La Rocque. 





Helen has twice as many dimes as nickles. 
20090908 

From Dan: Helen has twice as many dimes as nickles. She has 5 more quarters than nickles. She has $4.75. How many nickles does she have? I know she has 14 dimes, 7 nickles and 12 quarters. How do you put this into an algebra equation? Answered by Stephen La Rocque. 





Nickels and dimes 
20090903 

From MATTHEW: mike has 3 times as many nickels as Larry has dimes. Mike has 45 cents more than Larry. How much money does Mike have? Answered by Penny Nom. 





Nickels, dimes and quarters 
20090902 

From danielle: In changing a $5 bill, Sarah received nine more dimes than nickles and seven fewer quarters than dimes. How many coins of each type did she receive? Answered by Penny Nom. 





Investing in four accounts 
20090829 

From Kenneth: Hello:
An investor wants to divide $1000.00 into four amounts or accounts  one account earning 2%, the second account earning 5%, the third earning 9%, and the fourth earning 12%. He wants the overall total return to equal 5%.
What are some of the monetary amounts that can be invested into these four accounts to earn him the 5% total return, 5% of $1,000.00? Answered by Penny Nom. 





Chickens and pigs 
20090828 

From David: A farmer has a number of chickens and pigs. There are 24 heads and 80 ft.
How many pigs and how many chickens are there? Answered by Robert Dawson. 





Linear equations 
20090823 

From shwetha: The length of a rectangle is greater than the breadth by 18 cm. If both length and breadth are increased by 6 cm then area increases by 168 cm square. Find the length and breadth of the rectangle. Answered by Stephen La Rocque. 





Golf for 15 
20090818 

From Judy: We have a group of 15 golfers that play a scramble with groups of 3. The problem is we play for 14 weeks. We want every
player to play at least once with everyone and no more that 3 times. I am working on this and have just about accomplished
the schedule, but with a few playing more than 3 times. I'm sure there must be some mathematical calculation to do this but I
have yet to figure it out. Answered by Victoria West. 





Big and small widgets 
20090817 

From Leanne: A machine makes big widgets. Another machine makes small widgets. 3 small widgets have the same mass as 2 big widgets. It takes the same amount of time to make 3 big widgets as it does to make 5 small widgets. The machines start at the same time and make widgets until the total mass of all the widgets made is equal to the mass of 380 small widgets. What is the total number of widgets made? (Please include workings). Answered by Penny Nom. 





A walkway around a flower garden 
20090801 

From Barbara: A rectangular flower bed measuring =C2=A0 10 feet by 15 feet =C2=A0 has a surrounding walkway on all sides that measure 186 square feet. How wide is the walkway? Answered by Harley Weston. 





Two word problems 
20090731 

From Lee: 1) a student saved $50.25 in one month. at that rate how long will it take
the student to save $700?
2) for summer job, martin shampooed rugs. he could finish a 4mx 4m rug in 30 min.
his supervisor could finish a similar:smaller rug in 20 min. how long would
it take for them to finish the rug if they worked together? Answered by Robert Dawson. 





A father and son problem 
20090723 

From yomi: five years ago, a father was 3 times as old as is son, now their combines age's amount 110 years. what is the present age of the father? Answered by Penny Nom. 





Buying pens and staplers 
20090722 

From Ellen: one more math question,
six pens and four staplers cost $7.10. four pens and seven staplers cost $9.50
find the cost of one pen and one stapler. Answered by Penny Nom. 





Selling fish 
20090722 

From Hemantee: A fishmonger bought 150kg of fish. he sold 70%of it at the price of Rs90 per kg and the rest at Rs 75 per kg. he made a profit of 42.5 per cent. how much did he pay for the fish. Answered by Penny Nom. 





The girl guides bake sale 
20090720 

From Barbra: here is two questions i need help with,
1.)A toastmasters tea was attended by 550 people. Students paid 75 cents for their
tickets, and the adults paid $1.20. if the recipts totaled $525, how many adults and how many
students attended?
2.) One cookie and six bars cost $2.00 at the girl guides bake sale.
At the same sale, three bars and six cookies cost $2.10. Find the cost of one cookie and the
cost of one bar. Answered by Penny Nom. 





Portion of Work 
20090717 

From Ellen: A girl can shampoo the dog, clean his ears, and clip his nails in 45 minutes.
Her sister can do it in 60 minutes. How long will the job take it they work together? Answered by Stephen La Rocque. 





The product of two consecutive integers 
20090713 

From kelly: the product of two consecutive integers is 9 less than the square of the second integer Answered by Penny Nom. 





A base 7 number and a base 9 number 
20090709 

From koteawarao: Find a base 7 threedigit number which has its digits reversed when expressed in
base 9.
ans: (281) base 7 and (182) base 9 Answered by Harley Weston. 





The sides of a triangle 
20090708 

From Susan: The second side of a triangle is 5ft more than the length of the first side. The third side of the triangle is 10ft less than the length of the first side.
The perimeter of the triangle is 61ft. Find the lengths of each side of the triangle.
Thank you so much! Answered by Penny Nom. 





Mowing 17 lawns 
20090618 

From kevin: I need help setting up a equation to solve the following question: If a gardener can mow 3 lawns in 7 hours, how long should it take him to mow 17 lawns. I can solve the problem, but I don't know how to set up the equation. Answered by Penny Nom. 





The dimensions of a rectangle 
20090530 

From Linda: A rectangle has a perimeter of 38 feet & an area of 48 square feet. What are the dimensions of the rectangle? Answered by Stephen La Rocque. 





Two trains 
20090518 

From chris: Train A passes a station at 3:15am going 40mph. Train B passes the same station at 3:27am going 50mph. At what time will Train B catch up with Train A? Answered by Stephen La Rocque. 





An afternoon at the races 
20090515 

From garths: A professional gambler was betting at a horse racing afternoon.
At the end of the first race he had doubled his money.
He bet R30 on the second race and tripled the money he came with.
He bet 54 on the third race and quadrupled (4 times) the money he came with.
He bet R72 on the fourth race and lost it all. But he still had R48 left.
How much money did he take to the race track? Answered by Harley Weston. 





A reward and a fine 
20090512 

From garth: A maths teacher promised a learner that she would pay him R8 for each problem solved correctly,
but she would fine him R5 every incorrect solution.
At the end of 26 problems neither owed any money to the other.
How many problems did the learner solve correctly? Answered by Robert Dawson and Penny Nom. 





A two goat problem 
20090427 

From Michael: if you have a goat tied to a pole at one corner of a square paddock with one length of a side being 24m.
what length must the rope be for the goat tied up to graze half the paddock?
and if another goat is placed on the opposite corner and same length what is the amount of area they share grazing ? Answered by Stephen La Rocque and Penny Nom. 





A word problem involving y = mx + b 
20090424 

From Devon: I need to put the following question in to y=mx+b form
I rent a gym for $150.00 for 30 students. Another time I rent the gym for @270.00 for 70 students. I need to also find a fixed rate. Answered by Stephen La Rocque. 





Nickles and dimes 
20090417 

From Emily: a vending machine contains nickels and dime coins which totals an amount of $14.50. There are 95 more nickels than the number of dime coins. How many of each coin does exist? Answered by Penny Nom. 





Three consecutive odd integers 
20090402 

From Brian: Find the greatest of three consecutive odd integers if the product of the second and third is 8 more than 13 times the first. Answered by Robert Dawson. 





A maxmin problem 
20090324 

From Jay: Determine the area of the largest rectangle that can be inscribed between the xaxis and the curve defined by y = 26  x^2. Answered by Harley Weston. 





The height of a mountain peak 
20090323 

From james: Can you please help us (my son Jim geometry) out with this problem, we
cannot seem to find the correct method of solving, not sure how to solve the
scalene triangle with what is given...if that's the correct method?? Can you
please explain how this is solved!!
Thank you so much,
Jim and son ! Answered by Harley Weston. 





Problem solving 
20090321 

From susie: the product of a number and 9 increased by 15 is the same as one half of the difference of eight and four times the number. Find the number. Answered by Stephen La Rocque. 





The perimeter of a rectangle 
20090318 

From marylyne: the perimeter of the rectangular is 70 meters. if the width is 40% of the length, find the dimensions? Answered by Penny Nom. 





Stacking eggs 
20090312 

From Prashanth: if you stack two eggs eah in row you must get 1 balance
if you stack three eggs eah in row you must get 2 balance
if you stack four eggs eah in row you must get 3 balance
if you stack five eggs eah in row you must get 4 balance
it goes on like 6 , 7 , 8 and finally
if you stack nine eggs eah in row you must get 8 balance
what would be the answer and how to reach it Answered by Robert Dawson. 





Three consecutive odd integers 
20090311 

From Susan: Find three consecutive odd integers such that the sum of the first, twice the second, and three times the third is 70 Answered by Penny Nom. 





Marcia's summer earnings 
20090311 

From Yasmine: Marcia saved money by working over the summer. Before school started, she spent 25%of the money of jewelry
and then 2/3 of the remaining money on a digital camera. She still had $213 left. How much money did she have
before she started shopping? Answered by Robert Dawson and Penny Nom. 





2 types of season passes 
20090309 

From Jaquanta: A local water park has 2 types of season passes. Plan A costs a one  time fee of $142 for admission plus $8 for parking every trip. Plan B costs a one  time fee of $56 for parking plus $25 for admission every trip. How many visits must a person make for plan A and plan B to be equal in value? Answered by Penny Nom. 





A walkway through a park 
20090307 

From felicia: a diagonal walkway through a park is 18 meters long. If the park is a square, how long is one of its sides to the nearest tenth of a meter? Answered by Penny Nom. 





The angles in a parallelogram 
20090303 

From dolly: having a timewith equations inequaltites and problem solving=
the sum of the measure of the angles of a parallelogram is 360.anglesa a and d , have the same measure as angle c and d,c is twice the measure of angle a, what is the angle for each. Answered by Penny Nom. 





Collecting an army 
20090225 

From bevaz: Question from bevaz, a student:
A ruler orders his chamberlain to collect an army from 30 houses. The servant goes to the first house alone and collects one man. At each house after that he takes the same number of men as he has already collected, so at the second house he goes with one other and so on. How many men did he collect in all? Answered by Penny Nom. 





Two pages are attendants of a king 
20090224 

From Lauren: Two pages are attendants of a king. For their service, one gets 13/6 dinaras a day and the other gets 3/2 dinaras. The first page owes the second 10 dinaras. Calculate when they will have the same amount. Answered by Penny Nom. 





Three people working in pairs 
20090221 

From bevaz: A and B can together do a piece of work in 6 days, B and C together in 20 days and C and A in 7.5 days. how long will they require separately for the work? Answered by Penny Nom. 





Washing the dishes 
20090220 

From rm: a woman washing a large number of dishes after a meal was asked how many people attended the meal.
she did not know but 'every two used a dish of rice between them, every three a dish for soup and every
four a dish for meat, and there were 65 dishes in all.' how many people were there? Answered by Robert Dawson. 





A dinner party 
20090218 

From will: You are serving 3 different entrees at a party. If 100 guests are having beef, 175 guests are having pasta, and 45 percent of the guests are having chicken how many guests are expected at this party? Answered by Penny Nom. 





Broken vases 
20090217 

From JC: Hello,
I need help with a question. It is said that a company delivers 1000 vases to a man. It charged $0.40 for every vase safely delivered.
But the company had to pay the man $5.10 for each broken glass.
If the man paid a total of $383.50 for the delivery, how many vases were broken?
Regs. ,
JC Answered by Penny Nom. 





Frogs and kangaroos 
20090216 

From Jenny: Albert, Bernard, Charles, Daniel and Ellie play a game in which each is a frog or kangaroo. Frogs' statements are always false while Kangaroos' statements are alwas true. 1. Albert says that bernard is a kangaroo. 2. Charles says that Daniel is a frog. 3. Ellie says that Alvert is not a frog. 4. Bernard says that Charles is not a kangaroo. 5. Daniel says that Elie and Albert are different kinds of animals. How many frogs are there? Answered by Penny Nom. 





A and B shared some beads. 
20090215 

From Nicholas: A and B shared some beads. A gave 1/3 to B, B will have 70 more than A. If A gave 1/5 to B, B would have 10 more than A. A have how many at first ? Answered by Penny Nom. 





A goat in a square paddock 
20090210 

From lachlan: A farmer uses a rope to tether a goat to a pole at the corner of a square paddock. The length of one side of the square is 24m.
a) If the length of the rope is 12m,what % of the paddock can the goat reach? is the answer 19.62 %?
b) If the farmer wants the goat to be able to graze exactly half the area of the paddock, what length must the rope be? Answered by Penny Nom. 





A rectangular park 
20090206 

From Debbie: A park named Writer's Rectangle opened in town. When asked about the dimensions of the rectangle, the city planner, responded with these clues: The diagonals of the rectangular park plus its longer sides together measure seven times one of the shorter sides. The length of one diagonal is 250 m longer than one of the shorter sides. Use this information to find the area of the park. Answered by Stephen La Rocque. 





Randy' age and Mandy's age 
20090203 

From carolina: Randy is 4 times as old as Mandy, in 12 years, Mandies age is half of Randy's . how old is each now? Answered by Penny Nom. 





Whitney's average test score was 79 
20090130 

From dawn: After 5 tests, Whitney's average test score was 79. After she scored 85 on the 6th test. What was her new average? Answered by Penny Nom. 





Mixing candy 
20090127 

From adriana: The question says:
that a merchant wishes to mix candy worth 45 cents per pound, with some candy that costs 80 cents per pound. this will create a mixture of candy that sells for 65 cents per pound. there is a total amount of 350 pounds of candy.
What i need to know is:
The amount of pounds of candy at 65 cents per pound? and
The amount of pounds of candy at 80 cents per pounds? Answered by Harley Weston. 





Probability and birthdays 
20090122 

From La: Neglecting the effect of leap years, what is the chance that, of 6 people selected at random, 2 will have the same birthday? Answered by Penny Nom. 





The dimensions of a pool 
20090118 

From denise: a rectangular swimming pool is three times as long as it is wide. if the perimeter of the pool is 320 feet, what are its dimensions Answered by Penny Nom. 





Problem solving with fractions 
20090116 

From Linda: Sam and Mary each owned onehalf stock in a printing company. Sam sold 2/5 of his stock to Mary. What fractional part of the printing business does Mary now own? Answered by Stephen La Rocque. 





Two methods of payment 
20090113 

From adjoa: owen was offered $225.00per week plus 3%on sales, or 15%of sales with no salary. How much must he sell before the second method of payment gives him the highest pay? Express your answer to the nearest dollar. Answered by Penny Nom. 





Lita and Rose start jogging on a 110 m circular track 
20090113 

From Narcisa: Lita and Rose start jogging on a 110 m circular track. They begin at the same point, but jog in opposite directions, lita at 8/3 meters per second and rose at 7/3 m per second. Find the number of times they they will pass each other during the first 15 minutes of jogging? Answered by Robert Dawson. 





A Tshirt fundraiser 
20090111 

From Andre: Lou's class is selling Tshirts for a fundraiser. The supplier charges 750$ for the initial design and the setup plus 5$ for each imprinted shirt. The students sell the shirts for 15$ each.
a)How many Tshirts do the students need to sell to break even?
b)How much profit will the students make if they sell 150 shirts? Answered by Harley Weston. 





Who am I? 
20090109 

From daphne: im a 2digit number less than 85.the sum of my digits is 9.the number in my ones place is twice my tens digit. who am i? Answered by Robert Dawson and Harley Weston. 





What day of the week will it be? 
20090109 

From dan: suppose 3 days ago was a wednesday. what day of the week will 365 days from today be? Answered by Robert Dawson. 





Brothers and sisters 
20090109 

From Jade: Pat, Joe, Dave,Yoly, Dolor and Alma are three brothers  and sister  pairs who
play double tennis. Brother and sister ca not play in the same pair. Pat and Yoly
play Dave and Dolor on one day. Dave and Yoly play Joe and Alma on another
day. Name each brother  and sister pair, in any order. Answered by Robert Dawson. 





When is Sean's birthday? 
20090109 

From Robin: Sean is 4 months older than Tony. Mia is 6 months younger than Tony. If Mia's birthday is in April when is Sean's? Answered by Robert Dawson. 





Eric bought 3 sweaters and 1 pair of pants 
20090101 

From maya: eric bought 3 sweaters and 1 pair of pants. Each sweater cost d dollars and the pants cost 20 dollars. Eric spent a total of 95 dollars. The equation below can be used to determine the cost of each sweater. what is the answer? Answered by Penny Nom. 





Two rectangular plots have the same area 
20081223 

From Jason: Two rectangular plots have the same area. The first has a perimeter of 40m while the second has a length 2m less than the first and a width 1m greater. Find the length and breadth of the first rectangle Answered by Stephen La Rocque. 





Quadratic equations arising from practical problems 
20081124 

From Lenval: Why do quadratic equations arising from practical problems often give physically impossible solutions such as negative distances, negative times or, say, a polygon with a negative number of sides? For example: "A river in flood carries a tree tsquared  23t metres downstream in t seconds. How long does it take for the tree to be carried 50 metres downstream?" This gives t=25 and t=2. Please explain the second 'solution', which is not physically possible. Answered by Chris Fisher and Victoria West. 





Juanita and Jim each think of a number. 
20081118 

From Maria: Juanita and Jim each think of a number. Juanita's number is 8 more than Jim's number. The product of the two numbers is 65. What is Jim's number? Answered by Penny Nom. 





Insulation in an attic 
20081118 

From Scott: A homeowner wishes to insulate her attic with fiberglass insulation to
conserve energy. The insulation comes in 40cmwide rolls that are cut
to fit between the rafters in the attic. If the roof is 6 m from peak to eave
and the attic space is 2 m high at the peak, how long does each of the
pieces of insulation need to be? Round to the nearest tenth. Answered by Harley Weston. 





A word problem about a regular pentagon 
20081116 

From Sandra: If the area of a regular pentagon is A=1.720a^2, in which a is one of the sides. Find the area of a regular pentagon with a side that measures 50cm. Answered by Chris Fisher and Penny Nom. 





A game for 5 players 
20081116 

From safdar: five players agreed that after every game, the loser doubles every body's money. they played 5 games and everybody lost once. after the 5 games, everybody had 4128. How much money did each of the players have before the game? show your work. Answered by Janice Cotcher and Harley Weston. 





This question needs to be thrown away 
20081113 

From ang: I'm a friend trying to help a friend in lower algebra. I feel like this question needs to be thrown away. It's so ill written.
Find an mathematical expression/equation:
Half of the quotient of the total of a number and negative six and a number less negative six is the ratio of a number to
a number more than negative seventeen Answered by Stephen La Rocque and Harley Weston. 





Mary and Jane on a halfmile track 
20081110 

From alan: mary is walking 15mph on a half mile track. jane is walking 12mph on a halfmile track.
how much time will it take mary to pass jane.? HOW MANY TIMES WILL MARY PASS JANE IN 1 HOUR? Answered by Chris Fisher and Penny Nom. 





Supplementary angles 
20081110 

From Anna: <A and <B are supplementary angles. Twice the measure of <B is onefourth the measure of <A. Find the measure of both angles. Answered by Penny Nom. 





The dimensions of a rectangle 
20081107 

From laela: A rectangle is 8 feet long and 6 feet wide.If the dimension is increased by the same number of feet,the area of the new rectangle formed is 32 square feet more than the area of the original rectangle.By how many feet was the each dimension increased? Answered by Penny Nom. 





Purchasing pens and pencils 
20081107 

From Maggie: A mechanical pencil costs 50 cents and a pen costs 25 cents. If I spend 5.00 on 17 pens and pencils, how many of each does that buy? Answered by Penny Nom. 





A rectangle is twice as long as it is wide. 
20081104 

From Nawal: A rectangle is twice as long as it is wide.
If both its dimensions are increased by 4 m,
its area is increased by 88 m ^ 2.
Find the dimensions of the original rectangle. Answered by Penny Nom. 





Separating variables 
20081104 

From Terry: by separating variables solve the initial value problem
(x+1)y' + y = 0 y(0) = 1 Answered by Harley Weston. 





Three consecutive odd integers 
20081103 

From kim: Determine three consecutive odd integers such that twice the sum of the second and third is 29 less than 5 times the first. Answered by Penny Nom. 





Nickels, dimes and quarters 
20081027 

From val: I would like help working out a math word problem. A collection of 30 coins worth $5.50 consists of nickels, dimes, and quarters. There are twice as many dimes as nickels. How many quarters. Could you teach me how to find this formula? Answered by Penny Nom. 





Three congruent rectangles 
20081027 

From Meagan: Here is my problem: Three congruent (nonsquare) rectangles are placed
to form a larger rectangle. [Two are oriented the same way and the
"stacked" while the third is rotated 90 degrees and placed next to the
other two.] The total area is 1350 square cetimeters. Square ABCD is
then created that has the same perimeter as the large rectangle that was
created. E is the midpoint of line CD and F is the midpoint of BC. Find the
area of triangle AEF. Answered by Penny Nom. 





The length of a rectangle is 6 inches less than 3 times its width. 
20081026 

From Angela: The length of a rectangle is 6 inches less than 3 times its width. Find the
dimensions of the rectangle if its area is 45 square inches. Answered by Penny Nom. 





The chairs on a ski lift 
20081021 

From Travis: If you are sitting on chair 33 of a ski lift, which is a loop.
Chairs are numbered consecutively, starting with 1.
Chair 97 passes you halfway up the ski slope.
How many chairs are on the lift? Answered by Penny Nom. 





How much does Luc pay for his tools?? 
20081020 

From imran: Luc makes $1 profit on each tool he sells. Marc makes a $2 profit while paying $5 less for his tools than Luc. Marc thus makes $6 more profit for every $100 invested. How much does Luc pay for his tools?? Answered by Penny Nom. 





Maximize revenue 
20081008 

From Donna: A university is trying to determine what price to charge for football tickets. At a price of 6.oo/ticket it averages 70000 people per game. For every 1.oo increase in price, it loses 10000 people from the average attendance. Each person on average spends 1.5o on concessions. What ticket price should be charged in order to maximize revenue.
price = 6+x, x is the number of increases.
ticket sales = 70000 10000x
concession revenue 1.5(70000  10000x)
I just do not know what to do with the concession part of this equation
(6+x) x (70000  10000x) I can understand but not the concession part please help. thx. Answered by Penny Nom. 





The break even point 
20081003 

From dina: virgin record company has just signed a new artist to its label. They have pais the new group 25000 dollars to record their album
and paid each band member 10000 dollars each. The band is not given
a commission on each cd sold or downloaded, therefore, each cd sold is profit earned by virgin. How
many cd's would they have to sell to break even if this new band has 5 members? Each cd is sold at the price of 20$. Answered by Penny Nom. 





A different approach to a word problem 
20081003 

From Kenneth: Sarah's age is 2/3 of Mary's age and 3/4 of Ruth's age. The sum of their ages is 46 years. How old is each? Answered by Penny Nom. 





Find an All Odd 4  Digit Number 
20081002 

From Denise: a number has 4 different odd digits. the difference between the greatest digit and the least digit is 6, the number is greater than 2,000 and less than 3,160. what is the number? Answered by Janice Cotcher. 





Working together but one person starts first 
20080930 

From David: Della can scrape the barnacles from a 70 ft. yacht in 10 hours using an electric barnacle scraper. Don can do the same job in 15 hours using a manual scraper. If Della started helping Don three hours after Don started scraping, how long will it take to scrape the entire boat? Answered by Penny Nom. 





What is the perimeter of the rectangle? 
20080927 

From Pauline: A rectangle has an area of 27 squared inches. the height is 3 times the base
What is the perimeter of the rectangle? Answered by Penny Nom. 





Working together 
20080922 

From Wade: My daughter and I are having problems with this question:
Maggie can mow the lawn in 6 hrs. If her sister, Julie, helps her, it only take 2 hrs. How long
does it take Julie to mow the lawn alone. Answered by Penny Nom. 





Geometry with A Ladder Using Trig Functions 
20080920 

From Please: A ladder makes an angle of 50 degrees with the ground. if the base of the ladder is 10 feet from the building, how high up the building does the ladder reach?
i saw that someone else had a similar question, but we arn't using the pythagorean therom. we are using trig functions. Most of the problems we are doing is with the tangent. so this one probably is too. Answered by Penny Nom. 





A father and daughter problem 
20080919 

From Lamarr: A father is four times as old as his daughter is now. In 20 years he will be
only twice as old as his daughter. How old are the father and daughter now? Answered by Penny Nom. 





Concert tickets 
20080918 

From Keisha: Gross Receipts. Six thousand tickets are to be sold for a concert,
some for $9 and the rest for $15each. If x is the number of $9 tickets
sold , write an algebraic expression that represents the gross receipts
from ticket sales, assuming all tickets are sold. Simplify the expression. Answered by Penny Nom. 





The Width of a Mown Strip of Lawn 
20080915 

From Rimi: USE FACTORING, QUAD FORMULA, AND COMPLETE THE SQUARE!
Chris cuts half a rectangular lawn, 40m by 30m, by mowing strips
of equal width around the perimeter. Jonah cuts the small rectangle
left. How wide a strip does Chris cut so that they share the work equally? Answered by Harley J Weston. 





Pages in a Book 
20080908 

From Pandora: Is there a easier way to explain to my child regarding "pages" problem  like when to add one? when to sub tract one?
John read 46 pages in his new book. If he began reading at the top of page 33, on what page did he finish?
and John needs to do 45 pages of problems in his workbook. He finished this assignment at the the bottom of page 99. On what gate did John begain?
Thank you. Answered by Walter Whiteley. 





An array of tulip bulbs 
20080906 

From Mary: My daughter had this problem on one of her tests. She forgot to ask her teacher what she did wrong. I understand she did not answer the question
in full, but what she did answer I feel is right.
Please explain to me
the correct answer. Thank you. Mary Answered by Harley Weston. 





Mowing a Lawn in Concentric Bands 
20080905 

From Mari: two kids are mowing half of their backyard which is rectangular with
dimensions 75 ft by 90 ft. The first kid starts mowing at a corner
gradually working his way toward the middle by mowing concentric
bands around the outside edges.If the mower cuts 3ft wide path,
at what point should the first kid stop and the second kid start mowing?
THANKS! Answered by Janice Cotcher. 





A word problem with three numbers 
20080902 

From Wanda: "Jabari is thinking of three numbers. The greatest number is twice as big as the least number. The middle number is three more than the least number. The sum of the three numbers is 75. Find the numbers." Answered by Victoria West. 





The saddle height on a bicycle 
20080831 

From David: The saddle height on a bicycle should be 109% of the inside leg measurement of the rider (http://www.harriscyclery.com). If the saddle height is 37 in., then what is the inside leg measurement?
I don't know how to set up the equation if you can teach me how to set it up it would be great thanks Answered by Harley Weston. 





A fraction word problem 
20080829 

From Sylvia: The denominator of a fraction is 1 less than 4 times the numerator. If the numerator is doubled and the denominator is increased by 6, the value of the resulting fraction is 2/5. Find the original fraction. Answered by Penny Nom. 





How old are Brett and Jenny ? 
20080828 

From Todd: Brett and Jenny are each 10 years old. The sum of their ages is 11.
Brett is 5 years older than Jenny. How old are they? Answered by Janice Cotcher and Victiria West. 





Abby has 45 coins 
20080828 

From Sonia: Use an algebraic approach to solve the problem. Abby has 45 coins, consisting only of dimes and quarters, worth $6.6. How many dimes and how many quarters does she have? Answered by Penny Nom and Victoria West. 





A triangular field 
20080815 

From joneka: Barb walked five times aroun a triangle field all together she walked 435 feet the first side of the triangle fiel is 23 feet the length of the other two sides are of the same measure. What are the dimensions of the triangle field? Answered by Penny Nom. 





Two problems involving reciprocals 
20080810 

From Dee: I have a few questions that im have trouble working out...
1. One number is three times another number; if each is increased by 1 the sum of the reciprocals is 10/21. Find the numbers
2.A tank can be filled by 2 pipes together in 6 hours; if the larger pipe alone takes 5 hours less than the smaller to fill the tank, find the time in which each pipe alone would fill the tank Answered by Penny Nom. 





Cost of pencil is rising every year since 7 years ago 
20080806 

From Mari: Cost of pencil is rising every year since 7 years ago. If the cost of
pencil last year was 60 cents which is the sum of the cost from the
last two previous years, what is the cost of the pencil now, the cost
seven years ago. Answered by Penny Nom. 





The product of the digits of a four digit number 
20080726 

From Pete: I am a student preparing for a competition and this was one of the prep problems: The product of the digits of a four digit number is 6x5x4x3x2x1. how many such numbers are there with this property? Answered by Stephen La Rocque. 





Three consecutive positive integers 
20080720 

From AC: find three consecutive positive integers such that the product of the first and third, minus the second, is 1 more than 4 times the third Answered by Penny Nom. 





Two numbers whose sum is 25 and whose product is 120 
20080710 

From Michelle: Solve the following problem in at least two different ways.
Find two numbers whose sum is 25 and whose product is 120.
I know how to solve this problem by creating two equations
x+y=25 and xy=120 and then use substitution.
Are there any different ways of solving this problem? Answered by Janice Cotcher and Penny Nom. 





Two trains 
20080707 

From Elisha: Trains at each end of the 50. km long Eurotunnel under the English Channel start at the same time into the tunnel. Find their speeds if the train from France travels 8. km/h faster than the train from England and they pass in 17 minutes. Answered by Janice Cotcher and Penny Nom. 





How many handshakes take place? 
20080626 

From Peter: Eight people of different heights are at a party. Each person decides to only shake hands with people shorter than him/herself. How many handshakes take place?
My math book says it is 0. Is it wrong? If so, what is the answer? Answered by Harley Weston. 





What is the number of miles traveled by each tire? 
20080626 

From Peter: A car is driven 40,000 miles using four tires and a spare tire. The tires are rotated so that each tire travels the same number of miles. What is the number of miles traveled by each tire? Answered by Penny Nom. 





Four fours 
20080625 

From jen: Use four 4's and some of the symbols: +,,X, / and (), to give expressions for the whole numbers from 0 through9. Example : (4X4+4)/4=5 Answered by Janice Cotcher. 





An 18,000 mile automobile trip 
20080623 

From rachel: two men were about to start on an 18,000 mile automobile trip. The tires on their car were each good for 12,000 miles but not a foot more. how many spares will they need to go 18,000 miles Answered by Stephen La Rocque. 





I will be x years old in the year x squared 
20080622 

From rachel: you probably know someone who will x years old in the year x squared. When was that person born? Answered by ha. 





All wiffs are miffs and all miffs are kiffs. 
20080608 

From Allison: All wiffs are miffs. all miffs are kiffs. There are 25 wiffs. There are 76 kiffs. 33 kiffs are not miffs. How many miffs are not wiffs? Answered by Penny Nom. 





Tyres in a shipping container 
20080514 

From Carlene: I need to work out how many tyres will go in a shipping container.
The shipping container is 10 foot long, 8 foot wide and 8.6 foot high.
The tyre is 175 millimeters across and it is 14 inches in tyre thickness.
How many tyres will fit in my container? Answered by Stephen La Rocque. 





How old are the sisters? 
20080511 

From George: Theresa is four years older than her younger sister Joni. Twelve years ago, she was twice as old as her sister.
Find the present age of the two siblings. Answered by Penny Nom. 





Fencing a triangular field 
20080429 

From Julieta: The area of a field shaped like a triangle is 750yards squared. One leg of the field is fenced with wood costing $5/yd. The remainder of the perimeter of the field is fenced with steel costing $10/yd. The perimeter of the field is 150yards. the total cost of the fencing is $1200.
a. What is the length of the leg fenced with wood?
b. what is the length of the leg fenced with steel? Answered by Penny Nom. 





How many candles are on dave's birthhday cake? 
20080423 

From karen: on daves birthday, his brother henry is 17 years younger than 3 times dave's age,. the boys father ,tim is 17 years older than twice henry's age if dave is 7 years younger than his brother.
how many candles are on dave's birthday cake? Answered by Chris Langdon and Stephen La Rocque. 





The sum of the ages of Petra and her mother is 45 
20080420 

From Wendy: The sum of the ages of Petra and her mother is 45. Her mother is 12 years more than twice as old as Petra. How old are Petra and her mother? Answered by Leeanne Boehm. 





A water alcohol mixture 
20080420 

From Mary: How many oz. of solution that is 90% alcohol ( and 10% water) is needed to be mixed with 5 ounces of a solution that is 50% alcohol in order to obtain a solution that is 80% alcohol? Answered by Penny Nom. 





The dimensions of a rectangle 
20080420 

From Brandy: Find the dimensions of a rectangle with a primeter of 54 cm if the length is 5 less than three times the width. Answered by Penny Nom. 





A square garden of tulips 
20080408 

From Vincent: Each year Brandon plants tulip bulbs in a square flower bed. This year Brandon's flower bed has 29 more bulbs than it had last year. If the flower bed is still square how many tulip bulbs are in it this year? Answered by Penny Nom. 





How much do the pumpkins weigh? 
20080405 

From Jose: Mr. Appleberry brought in pumpkins for science class, one for each group.
The fist task wa to weigh the pumpkins, but the scales they had wouldn't register
any weight under 7 pounds, and it seemed that two ot three pumpkins were under
that weight. The class decided that they could weigh the pumpkins two at a time,
so they weighed each pumpkin with each of other pumpkins.
The weights registered on the scale were:
7 pounds
8 pounds
9 pounds
10 pounds
11 pounds
12 pounds
How many pumpkins were there, and how much did each weigh? Answered by Penny Nom. 





How far is she from her starting point? 
20080330 

From Nancy: A child runs due east for 23.5m and then she runs 10.5m due south. How far is she from her starting point? Answered by Stephen La Rocque. 





A word problem about numbers 
20080324 

From kathy: five times a number minus a second number is 6. The sum of the numbers is 12. find the numbers Answered by Penny Nom. 





A word problem about a triangle 
20080323 

From kathy: The measure of the largest angle of a triangle is twice the measure of the second largest. The measure of the second largest is 20 degrees more than the measure of the smallest. Find the measure of each angle. Answered by Melanie Tyrer. 





A pen with 40 post on each side 
20080318 

From Manpreet: how many post do you need to make a pen with 40 post on each side Answered by Penny Nom. 





Find the present age of the two siblings 
20080311 

From jessica: Theresa is four years older than her younger sister Joni. Twelve years ago, she was twice
as old as her sister . Find the present age of the two siblings. Answered by Stephen La Rocque. 





Average speed up and down a hill 
20080309 

From Judith: An old brokendown ar has to travel a two miles route, up and down a hill.
Because it is so old, the car travels the first mile  the ascent  at an average
speed of fifteen miles per hour. How fast must it cover the second mile 
the decent  to achieve an average speed of thirty miles per hours?
(There is a missing variable, but what is it?) Answered by Penny Nom. 





One number is four less than five times another number 
20080305 

From alice: One number is four less than, five times another number. The total of the two numbers is 50. What are the two numbers? Answered by Penny Nom. 





A puzzle about hats 
20080303 

From Sylvia: There were 4 people sitting in a row, truing to win $50.00 from a riddle.
The one in front was wearing a red hat.
The second from the front was wearing a blue hat.
The third from the front was wearing a red hat.
The last was wearing a blue hat and is blindfolded.
Each of them were informed that they are all wearing a hat,
the last person is blindfolded and that there are 2 red and 2 blue hats. If they can guess the
colour of their hat, then they win the prize.
There was a long silence, then one of them guessed the color of his hat correctly. Who was it?
and explain why.
(note that they can only see the person in front of them and are not allowed to turn around and
see behind them.) Answered by Penny Nom. 





Time and a half 
20080301 

From Travis: Bill receives time and a half for working overtime. If Bill is paid $55 for each hour of overtime, how much is his regular hourly wage? Answered by Stephen La Rocque. 





TV watchers on Thursday and Saturday 
20080228 

From flor: Thursday is the most watched night on television with 20 million more viewers than Saturday. the total for both nights is 102 million. how many viewers watch on each of these nights? Answered by Penny Nom. 





3 consecutive odd integers 
20080228 

From Pat: For 3 consecutive odd integers, twice the first integer, plus 5 more than the second integer, plus three less than four times the third integer equals 85. Find the 3 consecutive odd integers. Answered by Penny Nom. 





A triangle problem 
20080228 

From Jessica: Triangle ABC Angle C is 3 times angle A angle B is 30 degrees less than angle C what are the measurements of the angles
I have the measurements and I have the Equation but I can't figure out quite how to solve it the proper way Answered by Stephen La Rocque. 





Peg has 12 more cases to unload than Mike 
20080220 

From brianda: Peg has 12 more cases to unload than Mike. They have a total of 150 cases to unload. How my cases does each have to unload? Answered by Penny Nom. 





I am a 4digit number 
20080212 

From Nickie: I am a 4digit number with no repeating digits. I am divisible by 5, my first two digits (left to right) make a number divisible by 3, and my first three digits make a number divisible by 4. Also, my digits have a sum of 19 and I have the digit 7 in the thousands place. Who am I? Answered by Penny Nom. 





The angles in a parallelogram 
20080211 

From lauren: if the sum of the measures are 360 in a parallelogram. a and d are same measures, c and b are same too. If c is twice the measure of a what are all the angles? Answered by Penny Nom. 





A square and an equilateral triangle 
20080210 

From Emily: A square pen and a pen shaped like an equilateral triangle have equal perimeters. Find the length of the sides of each pen if the sides of the triangular pen are fifteen less than twice a side of the square pen. Answered by Stephen La Rocque. 





A 24 hour clock 
20080131 

From CARLA: at a certain time i looked at a 24hour digital clock and noticed some things about the time. (1 The number in the hours section plus the number in the minutes section makes 60.(2 One of the digits in the minutes section is the square root of the other digit in the minutes section.(3 The sum of the digits in the minutes section is the number in the hours section reversed. what is the time? Answered by Penny Nom. 





A car goes 15 miles on a gallon of gas 
20080126 

From Raven: A car goes 15 miles on a gallon of gas when it goes 50mph. When the car is driven 60mph it only goes 80% as far.
How far will it travel on a gallon of gas at 60mph?
I solved this two ways:
15 * .80 = 12 It goes only 12 miles or x/60 = 15/50 which is x = 12
This answer in the book is 4/5 * 15 = x. Then x = 12
How did they come up with 4/5? Answered by Penny Nom. 





Three consecutive odd integers 
20080124 

From daniel: find three consecutive odd integers such that three times the second minus the third is 11 more than the first.
help! i have x+1, x+3, x+5 as my 3 odd integers is this correct its been a while. Answered by Penny Nom. 





A toad climbs the stairs 
20080122 

From Kate: The question is:
A small toad is sitting at the bottom of the stairs. He wants to get to the 10th step, but is having some difficulty. He jumps up 2 steps and then back 1 each time. How many jumps will he take to reach the 10th step? Answered by Stephen La Rocque and Penny Nom. 





A word problem 
20080118 

From Marouf: How can you make a word problem for 6 2/3 and solve the word problem? I'm having trouble. Please help Answered by Stephen La Rocque. 





Two bikers race on a circular track 
20080117 

From Abby: Two bikers race on a circular track. Biker A can circle the track in 8 minutes, and Biker B can circle the track in 6 minutes. From the start of the race, how many minutes will it be before Biker B overtakes Biker A? Answered by Stephen La Rocque and Penny Nom. 





8 workers dug 3/8 of a tunnel in 10 days 
20080115 

From Marc: 8 workers dug 3/8 of a tunnel in 10 days. If the need to finish the remaining 5/8 of the tunnel in 3 1/3 days, how many more workers must they hire? Answered by Penny Nom. 





Two rectangles 
20080115 

From Paul: If the smaller dimension of a rectangle is increased by 3 feet and the larger
dimension by 5 feet, one dimension becomes 3/5 of the other,
and the area is increased by 135 square feet. find the original dimensions Answered by Penny Nom. 





The sum of two numbers is 36 
20080114 

From May: The sum of two numbers is 36.
Their product is 320.
What are the two numbers? Answered by Penny Nom. 





What year were the girls born in? 
20080106 

From Nyra: Christmas 2004 was over and three teenagers were looking forward to their birthdays. Eric's was in February and Lisa's and Tammy's in January. Tammy is 8 weeks older than Eric, but 3 days younger than Lisa. What year were the girls born in? Answered by Claude Tardif. 





A rectangle is three times as long as it is wide. 
20071231 

From Robert: A rectangle is three times as long as it is wide. If the length is decreased by 2 cm and the width is increased by 3 cm, the new rectangle has an area of 42 cm. What are the dimensions of the original rectangle? Answered by Penny Nom. 





Sally, Charlie and Snoopy in a race 
20071229 

From Marie: Sally and Charlie are having a race. Charlie gets a 900 foot lead and runs 8
inches per second. Sally begins at the starting line and runs at a rate of 5 ft per
second. Charlie's dog is also in the race. Snoopy starts 1100 feet ahead of Sally and runs
toward the starting line at a rate of 1 foot per second.
When will Charlie and Snoopy past each other and how far will they be from the starting line? Answered by Penny Nom. 





Three workers working together 
20071218 

From Rajesh: Worker A can do a piece of work in 15 days, worker B in 12 days, and worker C in 10 days. Worker A works 2 days, worker B 3 days, and worker C 3 days. In what time can worker A and worker B finish the job by working together? Answered by Penny Nom. 





How many houses must they paint? 
20071212 

From Natalie: The question is: Four boys work together,painting houses for the summer.For each house they paint they get 256 pounds.
If they work for four months of the summer and their expenses are 152
pounds per a month, how many houses must they paint for each of them
to have one thousand pounds at the end of the summer? Answered by Penny Nom. 





Find the perimeter of the original rectangle. 
20071211 

From Hannah: The area of a rectangle is 360 square meters. If the rectangle's length is increased by 10 meters and the width is decreased by 6 meters, its area does not change. Find the perimeter of the original rectangle. Answered by Melanie Tyrer. 





Delivering microwave ovens 
20071202 

From Barbara: Fernando and Kevin are delivering microwave ovens to a local appliance store, whose freight elevator can hold no more than 900 pounds. If Fernando weighs 180 pounds, Kevin weighs 240 pounds, and the microwave ovens weigh 30 pounds each, how many microwaves can Fernando and Kevin deliver at one time if they must ride in the elevator as well? Answered by Stephen La Rocque. 





Elimination of mayan prisoners 
20071119 

From Jim: An evil Mayan emperor decides to make an example of 1,000 prisoners. He stands them in a circle with numbers one to a thousand marked on their shirts. He then starts counting: "one in, two, in three out" The third man is immediately executed. This continues round and round and round the circle. While the number in the circle shrinks, every third prisoner is pushed out and executed. And it continues even when there are only two prisoners left alive. What number is on the last prisoner's shirt? Answered by Victoria West. 





Red balls and blue balls 
20071118 

From Md: In a group of 15, 7 have Red Balls, 8 have Blue Balls and 3 have neither.
What fraction of the group has both Red Balls and Blue Balls? Answered by Stephen La Rocque. 





Red hens and white hens 
20071118 

From Rapin: In 15 days, 4 white hens and 3 red hens lay eggs equal to 3 white hens
and 5 red hens lay eggs in 12 days , how many days that white hens can
lay eggs the same amount as red hens lay eggs in 20 days ? Answered by Steve La Rocque and Penny Nom. 





A quadratic function word problem 
20071112 

From liz: A kernal of popcorn contains water that expands when the kernal is heated,
causing it to pop. The equations below give the "popping volume"y(in cubic centimeters per gram)
of popcorn with moisture content x(as a percent of the popcorn's weight).
hot air popping: y = 0.761x^2 + 21.4x94.8
hot oil popping: y = 0.652x^2 + 17.7x 76.0
A) for hot air popping, what moisture content maximizes popping volume? What is the maximum volume?
B) For hot oil popping, what mositure content maximizes popping volume? What is the maximum volume?
C) the moisture content of popcorn tyipcally ranges from 8% to 18%. Graph the equations for hot air and hot oil popping on the interval 8 less then or equal to x and less then or equal to 18.
D) Based on the graphs from part(c), what general statement can you make about the volume of popcorn produced from hot air popping verus hot oil popping for any moisture content in the interval8 less then or equal to x and less then or equal to 18. Answered by Penny Nom. 





I have 23.50 in quarters and dimes 
20071109 

From hannah: i have 23.50 in quarters and dimes. if i have 15 more dimes than
two times the amount of quarters i have, how many coins do i have total? Answered by Penny Nom. 





A rectangularshaped bedroom 
20071108 

From Svitlana: Professor Reissig is doing renovations on one of the rectangularshaped bedrooms in his house. He is putting up a border around the room. The room’s length is seven feet more than twothirds of its width. The area of this bedroom is one hundred eighty square feet. If the border costs $1.25 per six inches, what is the minimum cost for the border? Answered by Penny Nom. 





Chris has twice as many $1 bills as pennies 
20071102 

From vicky: Chris has twice as many $1 bills as pennies, twice as many dimes as he has $10 bills, and twice as many pennies as he has dimes. How much money does he have? Answered by Penny Nom. 





The length of a rectangle is twice the width 
20071026 

From Tami: The length of a rectangle is twice the width. The number of square units in it's arear is four times the number of units in it's perimeter. What are the dimensions of the rectangle? Answered by Penny Nom. 





The dimensions of a rectangle 
20071014 

From Elizabeth: The perimeter of a rectangle is 20m. The area is 20sqm. Calculate the dimensions of the rectangle. Give your answers correct to two decimal places. Answered by Penny Nom. 





Nickels, dimes and pennies 
20071014 

From tom: you have $1.00 and 1/5 of it is dimes, 2/15 is nickels, and 2/3 is pennies. How many coins of each are there. how do i set it up to solve this problem. thanks, tom Answered by Penny Nom. 





How many students attended the gettogether? 
20071011 

From Diane: Some students planned for a gettogether.
The budget for food was $500. Five of the students failed to come
because of the distance and therefore the cost of food for each
member increased by $5.
How many students attended the gettogether? Answered by Stephen La Rocque. 





Problems solved using quadratic equations 
20071007 

From Lisa: a. Two positive numbers differ by 5. Their product is 234. What are the two numbers?
b. The sum of two numbers is 12. Their product is 30. What are the two numbers?
c.Two numbers differ by 5. Their squares differ by 55. What are the two numbers?
d. The sum of two numbers is 15. Their product is 56. By forming an equation, find the two numbers. Answered by Penny Nom. 





Working together 
20070921 

From farah: A can do a piece of work in 10 days while B can do the same work in 15 days . They work together for 5 days and the rest of the work is done by C in 2 days . If they get 400$ for the whole work , what should be A's share. Answered by Harley Weston. 





A word problem 
20070917 

From Martin: One more than the difference between 18 and seven times a number is 9 Answered by Stephen La Rocque. 





Taping the gym floor 
20070917 

From Marina: You are helping the coach tape lines on the gym floor to divide the length of the gym into 8 lanes of the same size. If it takes one minute to tape a line,how long will it take to do the job. State the strategy /strategies you used and why? Answered by Penny Nom. 





How many vertices are there? 
20070910 

From Makayla: I've just started the 4th grade and I am having trouble with a question on my homework. The questions is: Carrie is arranging sticks to make shapes. she has made a closed figure, with 10 sides How many vertices are there? I believe the answer is ten but I'm not sure. Answered by Stephen La Rocque and Walter Whiteley. 





How many stairs in the flight are stepped on exactly once? 
20070903 

From Bill: Four friends are racing together down a long flight of stairs. A goes 2 steps at a time, B 3 at a time, C 4 at atime and D 5 and at a time. The only steps on which all four tread are the top one and the bottom one. How many stairs in the flight are stepped on exactly once. Answered by Harley Weston. 





A word problem 
20070831 

From Regian: How can I write a word problem for the following numerical expression
3 (4+3)+2
And then how do I simplify the expression Answered by Penny Nom. 





What are the two numbers? 
20070813 

From Tiffany: The sum of two number is 29.The difference is 1. What are the two numbers? Answered by Stephen La Rocque, Melanie Tyrer and Penny Nom. 





At what speed does Chuck travel? 
20070727 

From Jessica: Chuck and Dana agree to meet in Chicage for the weekend. Chuck travels
224 miles in the same time that Dana travels 204 miles. If Chuck's rate of travel
is 5 mph more than Dana's, and they travel the same length of time, at what speed
does Chuck travel? Answered by Harley Weston. 





What are the dimensions of the field? 
20070723 

From Debourah: a soccer field is 1080 square meters the width is 2 meters less than onethird the length. What are the dimensions of the field? Answered by Penny Nom. 





A square and an equilateral triangle have the same perimeter. 
20070702 

From eve: I am trying to help my daughter with the following problem: A square and an equilateral triangle have the same perimeter. The sum of one side of the square and one side of the triangle equals 28 cm.
Find the sides of the figures. Answered by Penny Nom. 





A ten foot long board is cut into three pieces 
20070612 

From Cynthia: How do I solve this problem?
A ten foot long board is cut into three pieces. The second piece is half
as long as the first. The third piece is 4 1/2 longer than the second.
How long is the first? Answered by Penny Nom. 





What is the total weight of the fish? 
20070608 

From Mike: The tail of a fish weighs 9 oz. The head weighs as much as the tail and half of the body. The body weighs as much as the head and tail combined. What is the total weight of the fish? Answered by Stephen La Rocque. 





Optimization  carrying a pipe 
20070505 

From A student: A steel pipe is taken to a 9ft wide corridor. At the end of the corridor there is a 90° turn, to a 6ft wide corridor. How long is the longest pipe than can be turned in this corner? Answered by Stephen La Rocque. 





The sum of the ages of petra and her mother is 51 
20070505 

From Natakie: the sum of the ages of petra and her mother is 51. Her mother is 12 years more than twice as old as petra.
how old are petra and her mother. Answered by Stephen La Rocque. 





Comparing two pay scales 
20070503 

From san: Mable is offered a job selling magazine subscriptions. She has the choice of two pay scales.
Pay scale 1:
She can be paid $0.65 for each subscription she sells.
Pay scale 2:
She can be paid $0.10 for the first subscription, with the wage gong up $0.05 more for each subscription after the first.
For her first sale she would make $0.10, for her second sale she would make $0.15, for her third sale she would make $0.20,
and so on.
Please compare and analyze the two scales. Which scale is better? Answered by Penny Nom. 





A cylinder inside a sphere 
20070425 

From Louise: i need to find the maximum volume of a cylinder that can fit inside a sphere of diamter 16cm Answered by Penny Nom. 





A corny problem 
20070421 

From Robby: My name is Robby and I need help with a problem. I have found at
least 4 correct answers, but I can't figure out how I got the answer or
if there is a formula that I can use. I got my answers by trial and
error. Problem: One hundred bushels of corn are to be divided among
100 men, women, and children. Men get 3 bushels each. Women get two
bushels each. Children get 1/2 bushel each. How can the bushels be
distributed with no leftovers? Is there more than one solution?
So far, I have 4 answers: 8 men,20 women, and 72 children,
2 men, 30 women, and 68 children, 5 men, 25 women, and 70 children, and
11 men, l5 women, and 74 children. I need to know if there is a formula
to use, or if it's just trial and error, or if a pattern is involved. Answered by Stephen La Rocque and Penny Nom. 





By how many feet was each dimension increased? 
20070418 

From Becca: A rectangle is 8 feet long and 6 feet wide. If each dimension is increased by the same number of feet, the area off the new rectangle formed is 32 square feet more than the area of the original rectangle. By how many feet was each dimension increased? I need a diagram and 5 or more sentences for an explanation. Thanks! Answered by Stephen La Rocque. 





One number is 12 more than another. 
20070414 

From Devon: One number is 12 more than another. The sum of the smaller number and twice the larger number is 39. Find the larger number. Answered by Penny Nom. 





Word problems 
20070413 

From Perla: 1.A school district is proposing a 5% increase in the numbber of days in a school year. How long would a school year be with the proposed increase?
2. Keikio spent the day bird watching and counted 34 more birds in the morning than in the afternoon. If she counted a total of 76 birds, how many birds did she count in the afternoon? Answered by Penny Nom. 





Word problems 
20070409 

From Danielle: I am teaching a student who cannot understand which operation to use when doing word problems. I have tried a number of different ways to show him...any suggestions? Answered by Haley Ess. 





How far apart are the cars? 
20070407 

From ian: 2 cars set off in opposite directions and travel for 6 miles,
they both take a left turn, and travel for a further 8 miles...........
how far apart are the cars???
a) 10 miles
b) 22 miles
c) 20 miles
d) 18 miles Answered by Penny Nom. 





Inscribed square in inscribed circle 
20070325 

From Confuzzled: "The largest possible circle is drawn inside a square. Then the largest possible square is drawn inside this circle. What is the area of the inner square as a fraction of the area of the outer square?"
This is a question from the Grade 8 Gauss contest and I don't know how to work it out without drawing it. My teacher says it's possible but I still don't get it. Please help!!! Answered by Stephen La Rocque. 





Nickels, dimes and quarters 
20070318 

From Alexandra: Ellen has two more nickels than dimes and three more quarters than nickels. She has $3.35 in all. How many coins of each type does she have? Answered by Penny Nom. 





Two busses 
20070315 

From Devon: A bus leaves a station at 1 p.m., traveling west at an average rate of 44 mi/h. One hour later a second bus leaves the same station, traveling east at a rate of 48 mi/h. At what time will the two buses be 274 mi apart? Answered by Steve La Rocque and Penny Nom. 





Who won the backstroke? 
20070226 

From Timothy: Three girls held a series of swimming races among themselves. They decided to award a positive whole number of points for finishing first, second and third, where the number of points for first was more than the number for second, which was more than the number for third. The same number of points was awarded for the place in each race. There were no ties.
The first race was breaststroke. Altogether Sarah accumulated 20 points, Michelle 10 points and Catherine 9 points. If Sarah did not win the backstroke race, who did win the backstroke? Answered by Penny Nom. 





How old are they now? 
20070226 

From Ali: Please help us. My daughter can't get this answer. The sum of Louise's age and Todd's age is 34. 5 years ago the sum of twice Louise's age and 3 times Todd's age was 61. How old are they now? Answered by Haley Ess and Steve La Rocque. 





Alligation 
20070209 

From Shanah: Orders: 360 mL of 75% acetic acid Stock: 99% acetic acid and distilled water Find the volume of acetic acid and distilled water to get the needed concentration. Any help with this is greatly appreciated, Thanks Answered by Stephen La Rocque. 





Dividing money unequally 
20070206 

From Linda: I have a total of $13,826.48. It is to be divided by 15 kids  2 of the kids only get half of what the other 13 do  how much do the 13 get and how much does the 2 get? Thanks Answered by Haley Ess and Steve La Rocque. 





More on a man and his wife on an escalator 
20070202 

From Patrick: Hello, I was helping my son with a homework problem and came across a very similar on your site:
http://mathcentral.uregina.ca/QQ/database/QQ.09.01/monty1.html
We are trying to understand the answer shown. There seems to be leap, in the answer that isn't explained or we can't see it. Specifically in the answer it says:
"We know that the woman olny walks 21 steps to reach the top, and thus in the time she walks 7 more steps the escalator also goes up 7 steps. Hence the woman and the escalator are travelling at the same rate."
We understand that she still has 7 steps left, but how is it that you can conclude from that (or other factors) that during those 7 steps the escalator will also travel 7 steps.
Thanks in advance for any help you can offer. Pat Answered by Stephen La Rocque. 





Fencing a field 
20070201 

From Carol: "The area of a rectangular field is 1200m^2. Two parallel sides are fenced with aluminum at $20/m. The remaining two sides are fenced with steel at $10/m. The total cost of the fencing is $2200." What is the length of each side fenced with aluminum and steel? Answered by Stephen La Rocque. 





A right triangle 
20070129 

From Tayler: One leg of a right triangle is 8 cm. less than the hypotenuse while the other leg is 1 cm. less than the hypotenuse. Find the length of the hypotenuse. Answered by Penny Nom. 





The sum of the digits of a twodigit number is 13. 
20070127 

From Liz: The sum of the digits of a twodigit number is 13. If the digits are reversed, the new number is 9 more than the original number. Find the original number. Answered by Penny Nom. 





A word problem 
20070105 

From Harold: the sum of one number plus four less than five times another is 26. Answered by Penny Nom. 





The average of 3 tests 
20061212 

From Charles: If you average 84 on first three test and the first score was 67. The second score was 7 less than the third score. What was the score on the second and third test. Answered by Stephen La Rocque. 





A Norman window 
20061130 

From Joe: a norman window is a rectangle with a semicircle on top. If a norman window has a perimeter of 28, what must the dimensions be to find the maximum possible area the window can have? Answered by Stephen La Rocque. 





Two trains left the station at the same time and traveled in opposite directions. 
20061118 

From Tori: Two trains left the station at the same time and traveled in opposite directions. The E train averaged 130 km/h. The A train's speed was 110 km/h. In how many hours were they 480 km apart? Answered by Stephen La Rocque. 





Apples and plums 
20061113 

From Saif: the problem i am stuck with is, nicole buys 2.3kg apples 1.8kg plums she pays £7.18 total plums cost £2.20per kg cost 1kg apples what is the cost of 1kg of apples Answered by Stephen La Rocque. 





After how many hours will the class have been notified? 
20061110 

From Brittany: A college math class consists of 32 students. On Monday at 9:00 a.m., the teacher tells one student to notify other students that the test scheduled for Wednesday at 9:00 a.m. has been cancelled. The model for the number of students in the class who will have heard this information after t hours is N=3232e^0.02t. After how many hours will the class have been notified? Answered by Stephen La Rocque. 





A mixture problem 
20061105 

From Lynne Rae: How many kg of 30% salt solution by mass and 40% salt solution by mass should be mixed to form 200kg of 37% salt solution by mass? Answered by Penny Nom. 





Bill has four more dimes than nickels ... 
20061105 

From Allison: bill has four more dimes than nickels, and seven fewer nickels than pennies.he has a total of $3.35. how many of each kind of coin has he? Answered by Karen McIver. 





The sum of two numbers is 30 
20061103 

From GG: The sum of two numbers is 30 and the product of the same two numbers is 221. Find the two numbers. Answered by Stephen La Rocque. 





Paddeling on the Alleman River 
20061031 

From Anita: Len is planning a threehour trip down the Alleman River and back to his starting point. He knows that he can paddle in still water at 3 mph and that the rate of the current is 2 mph. How much time can he spend going downstream? How far downstream can he travel? Answered by Penny Nom. 





How much labor should the firm employ? 
20061028 

From Christy: A dressmaking firm has a production function of Q=LL(squared)/800. Q is the number of dresses per week and L is the number of labor hours per week. Additional cost of hiring an extra hour of labor is $20. The fixed selling price is P=$40. How much labor should the firm employ? What is the resulting output and profit? I am having a difficult time with this, HELP! Answered by Stephen La Rocque. 





Ridingcap's daughter 
20061023 

From Marcus: Ridingcap's daughter,whose real name was Coleen, set out for grandma's house again. This time she was delivering jam and jellies. First she stopped to see Mrs. Parsley,who took in grandma's mail while grandma was @ the hospital recovering from the wolf. Colleen gave Mrs. Parsley one third of the jars in her basket. Then Colleen set out again,and suddenly the wolf jumped out behind the bush and grubbed one half of the jars in Colleen's basket. When the wolf ran off, Colleen went on and gave Mr .Woodsman two thirds of what was left in her basket. Colleen had six jars of jam and jellies left for grandma. HOW MANY JARS DID COLLEEN LEAVE HOME WITH Answered by Stephen La Rocque. 





Word equations 
20061022 

From Samira: One half of a number is subtracted from the sum of onethird and onequarter of the same number. If the result is 16, find the number. Answered by Stephen La Rocque. 





Word problem 
20061022 

From Sabrina: Thomas bought a badminton racquet and paid for it in quarters. If Thomas had used nickels and dimes, he would have needed 20 more dimes than quarters and one more than twice as many nickels as quarters. How much much did the badminton racquet cost? Answered by Stephen La Rocque. 





Two word problems 
20061002 

From Eve:
1. A surveyor's map shows a plan for the rectangular rose garden whose area is
a^{2}+25ab350b^{2}. Find an algebraic expression for the length and width. If a=20 ft and b=10 feet, find the actual dimensions of the garden.
2.A square is enclosed in a circle. The area of the square is (4r^{2}32r+64)sq cm and the area of the circle is 484r^{2} sq cm. Write a polynomial in factored form to represent the difference of the two areas.
Answered by Stephen La Rocque. 





How long will it be before the two snails meet? 
20060921 

From Brett: Two snails are 8.5 feet apart. They start to crawl toward each other at the same time. One of them travels at the speed of 6 in. per minute, while the other zips along at 11 inches per minute. How long will it be before the two snails meet? Answered by Penny Nom. 





How much did I spend on the first trip? 
20060910 

From Alexander: I have $600 to spend.
I take 10 shopping trips.
Each trip I spend $10 more than the last trip.
How much did I spend on the first trip?
Answered by Stephen La Rocque. 





A triangle problem 
20060806 

From A student: A triangle is such that its medium side is twice as long as its shortest side, and its longest side is three times as long as its shortest side. The perimeter of the triangle is 54 yards. What are the lengths of the three sides? Answered by Penny Nom. 





Some word problems 
20060630 

From Oliver:
Question: I am a father of a 10 years old boy and sending this question from Bangkok, Thailand. I need solutions for the following:
1
Joseph and Peter spent $45 altogether.
Joseph and Harold spent $65 altogether.
If Harold spent 3 times as much as Peter, how much did Joseph spent?
I know the answer is $35 but do not know how to get to it.
2
. . .
Answered by Penny Nom. 





A jar contains 36.25$ 
20060612 

From Brunia: A jar contains 36.25$ in pieces of 0.10 and of 0.25$. If it there has 250 change pieces in all, how much there he has pieces of 0.25$ in the jar. Answered by Penny Nom. 





Tiling a floor 
20060608 

From Marguerite: A builder is adding a 20' X 28' addition to a house. He has two choices: he can use 8" X 8" tile @ $.98 a tile or 12" X 12" tile @ $1.98 a tile. How much money would he save by using the least expensive choice? Answered by Stephen La Rocque and Penny Nom. 





Three purses 
20060522 

From Marcee: If you take $20 from the first and put it into the second of three purses, the second would then contain 4 times as much as remains in the first. If $60 of what is now in the second is put into the third, the third will contain twice what is in the first and second together. Now, if $40 be removed from the third and put into the first, there will be half as much as in the third. What did each purse originally hold? Answered by Penny Nom. 





Three questions 
20060517 

From Diane:
Question:
I
What is the largest real number less than 10?
1 there is no largest real number less than 10 or
2 9
or
3 9.999...
II
Given that not (a and b) implies c.What does
(not c) imply ?
1a and b
2 (not a and b) or (a and not b)
3 (not a and b) or (a and not b)
4 a or b
III
What are the x and y intercepts of the equation
2x + 3y 6 =0 ?
1 x=3 and y=2
2 x=6 and y=2
3 3x + 2y =0
Answered by Paul Betts. 





Cutting a piece of PVC pipe 
20060503 

From Shonda: A plumber has a 10' piece of PVC pipe. How many 9/5 foot pieces can be cut from the 10' piece? Answered by Penny Nom. 





A word problem with fractions 
20060502 

From Stuart: I have 54 1/4 yards of material. i need to cut as many pieces as possible out of it that are 3 1/12 long. how many pieces
will you get and how much is left over? Answered by Stephen La Rocque. 





How many people are in the race? 
20060407 

From Marty: You're in a race with 1/5 of the racers ahead of you and 5/6 of them behind you. How many people are in the race? Answered by Penny Nom. 





Piecewise functions 
20060321 

From Kris: First Problem:
Southeast Electric charges .09 cents per kilowatthour for the first 200 kWh.The company charges .11 cents per kilowatthour for all electrical usage in excess of 200 kWh. How many kilowatthours were used if a monthly electric bill was $57.06? The answer I came up with is 360, is that right? and also how do I set it up in an equation form?
Second Problem:
A construction worker earned $17 per hour for the first 40 hr of work and $25.50 per hour for work in excess of 40 hr. One week she earned $896.75. How much overtime did she work? I came up with 8.5 hrs overtime worked. Again I don't know how to set up the equation to come up with the answer.
I need some pointers on how to figure out story problems! If you have any suggestions that would help me out I would be very grateful. Answered by Penny Nom. 





What percentage of the seniors polled yes? 
20060320 

From Jean: An equal number of juniors and seniors responded to the question, "Do you like math?" Each respondent said yes or no. If 70% of those who said yes were seniors and 80% of those who said no were juniors, what percentage of the seniors polled yes? Answered by Penny Nom. 





Back to the nines 
20060315 

From Victoria:
Can you answer this problem, does an answer exist?
 Get a set of numbers 19 !
 Using the whole set of nine number tiles (digits 19), try to arrange them to make three 3digit numbers so that the sum of the first two is the third.
Can this be done without carrying over? If not can it be done without carrying over into the hundreds column? Answered by Claude Tardif. 





Zhi Wei was born on christmas day in 1983. 
20060214 

From Clement: Zhi Wei was born on christmas day in 1983. His father shares the same birthday, but he was born in 1951. In which year will Zhi Wei's age be exactly 1/3 of his father's age? Answered by Stephen La Rocque. 





The box of maximum volume 
20060201 

From Elizabeth: A box factory has a large stack of unused rectangular cardboard sheets with the dimensions of 26 cm length and 20 cm width.
The question was to figure what size squares to remove from each corner to create the box with the largest volume.
I began by using a piece of graph paper and taking squares out. I knew that the formula L X W X H would give me volume. After trial and error of trying different sizes I found that a 4cm X 4cm square was the largest amount you can take out to get the largest volume. My question for you is two parts
First: Why does L X H X W work? And second, is their a formula that one could use, knowing the length and width of a piece of any material to find out what the largest possible volume it can hold is without just trying a bunch of different numbers until you get it. If there is, can you explain how and why it works. Answered by Penny Nom. 





Word problems 
20060127 

From Duk: One kind of candy sells for 90cents more a pound than another kind. A pound of each sells for a total of $5.10. What is the selling price of each kind?
A soft drink sells for 20 cents more than the deposit required on the bottle. The cost of the soft drink and the bottle deposit totals 70cents. How much is the soft drink? The bottle deposit? Answered by Penny Nom. 





Joey had 8 drinking glasses, all of different sizes. 
20051229 

From Danielle: Joey had 8 drinking glasses, all of different sizes. he has lined them up from smallest to largest and numbered them #1 (smallest) to #8 (largest). he knows that glass #4 holds 10 ounces and that glass #7 holds a pint, or 16 ounces. Now he wants to figure out how much all the others hold!
He experiments by filling up different glasses with water and pouring the water back and forth into other glasses. Her are his results: Answered by Penny Nom. 





Two dogs and a flea 
20051223 

From Michelle: Two dogs, each traveling at 10 ft/sec, run toward each other from 500 feet apart. As they run, a flea flies from the nose of one dog to the nose of the other at 25 ft/sec. The flea flies between the dogs in this manner until it is crush when the dogs collide. How far did the flea fly? Answered by Penny Nom. 





A rectangle has a length that is 7cm more than twice the width 
20051221 

From Stephanie: A rectangle has a length that is 7cm more than twice the width. The area of the rectangle is 60cm squared. Find the dimensions of the rectangle. Answered by Penny Nom. 





Skeeball 
20051221 

From Jenny: Kira and Dajuan decided to have a Skeeball contest. They each played one game to see who would get the highest score. A description of their contest follows: Answered by Denis Hanson. 





A word problem 
20051219 

From Karen: A package designer wants to protect an expensive book with a 5 cm wide cardboard rim. The area of the rim is equal to the area of the book. What is the length of the book? (The book is square) Answered by Penny Nom. 





A maxmin problem 
20051216 

From Julie: A car travels west at 24 km/h. at the instant it passes a tree, a horse and buggy heading north at 7 km/h is 25 km south of the tree. Calculate the positions of the vessels when there is a minimum distance between them. Answered by Penny Nom. 





Mrs. Faria lives on an island 
20051215 

From Julie: Mrs. Faria lives on an island 1 km from the mainland. She paddles her canoe at 3 km/h and jogs at 5 km/h. the nearest drug store is 3 km along the shore from the point on the shore closest to the island. Where should she land to reach the drug store in minimum time? Answered by Penny Nom. 





Pat invested a total of $3000 dollars 
20051214 

From Duane: Pat invested a total of $3000 dollars. part of the money yields 10 percent interest per year and the rest yields 8 percent interest per year if the total yearly interest is $256 how much did pat invest at 10 per cent and how much at 8 percent. Answered by Penny Nom. 





A long distance call 
20051205 

From A student: The Small World long distance phone company charges 55cents for the first minute of a long distance call and 23cents for each additional minute.
1. How much would a 10 minute longdistance call cost?
2. If a call costs $4.55. how long did the call last?
3. Write an equation for the total cost, C, of an mminute longdistance call. Answered by Penny Nom. 





Two word problems 
20051114 

From Jennifer:
1. Every other person on a school's parent advisory committee is surveyed to determine how many people support passage of a school bond to build a new elementary school. Is this a good sample? Why or why not?
2.What is the difference in elevation between the highest point in California,Mount Whitney,which towers 4421 meters above sea level, the lowest point in California,Death Valley, which lies 86 meters below sea level?
Answered by Harley Weston. 





A picture window 
20051114 

From Marcos: The length of a picture window is 2 feet longer than twice its width. If the diagonal of the window is 13 feet, find the dimensions of the window. Answered by Penny Nom. 





Add one 1 at the beginning and at the end of a number 
20051113 

From Samuel: If we add one 1 at the beginning and at the end of a number, this number is increased by 14789.
What is the sum of the digits of the number? Answered by Penny Nom. 





Mario is 16 years older than his youngest sister, Mercedes. 
20051108 

From Jennifer: Mario is 16 years older than his youngest sister, Mercedes. Together, their ages total 36 years . How old is each person? Answered by Paenny Nom. 





How many passengers boarded the plane in Phoenix? 
20051103 

From Vish: Passengers boarded a plane in Phoenix. In Dallas 1/2 of the passengers got off and 4/5 of the original number got on. In Memphis 3/4 of the passengers got off and twice the number of remaining passengers got on. In Chicago 2/3 of the passengers got off the plane leaving 39 passengers. How many passengers originally boarded the plane in Phoenix? Answered by Penny Nom. 





Writing an equation 
20051101 

From Richie: A man's electric bill is $23 less than his gas bill. The two utilities cost him a total of $109. Find the amount of his gas bill. Answered by Penny Nom. 





sin(kx) = x 
20051020 

From David: What is an integer value for k so that sin(kx) = x has exactly 2005 solutions? How does one arrive at the answer? Answered by Harley Weston. 





A boat weighs 1500 lb more than its motor ... 
20051017 

From Dimitri: A boat weighs 1500 lb more than its motor and 1900 lb more than its trailer. Together the boat and motor weigh five times as much as the trailer. How much does the boat weigh? Answered by Penny Nom. 





Jim is travelling from Toronto to Ottawa 
20050815 

From Eleanor: Hi! I am looking for an easy way to solve this type of question: Jim is travelling from Toronto to Ottawa, a distance of 435 miles. He travels part of the way at a speed of 100 km/h and because of an accident, he uses a secondary road and travels at 70 km/h. If the trip took him 6.5 hours, how far did he travel on each of the two roads. Answered by Penny Nom. 





Trading fish for bread 
20050225 

From Mike: Byron lives where people trade goods they produce for other things they
need. He has some fish and wants to trade them for bananas. He finds
the following:
5 fish = 2 loaves of bread
6 oranges = 2 melons
1 loaf of bread = 1 banana and 3 oranges
4 loaves of bread = 14 oranges
How many bananas can Byron get with 5 fish? Answered by Penny Nom. 





By how much is 100 multiplied or divided,... 
20050127 

From Benedict: By how much is 100 multiplied or divided, so that whether the number obtained is divided by 5 or 7, there will be a remainder of 1 and so that at the same time, the first quotient is greater by 4 than the second? Answered by Penny Nom. 





Profit 
20050110 

From Abraham: The profit a coat manufacturer makes each day is modeled by the equation P(x)=x2+120x2000, where P is the profit and x is the price for each coat sold.For what values of x does the company make a profit?
I don 't understand this problem(how to do it) and hope you can help me. Answered by Penny Nom. 





Planting trees 
20041115 

From Heather: Design a plan of how it would be possible to plant 10 trees in 5 rows, and have 4 trees in each row. Answered by Penny Nom. 





A mixture problem 
20040930 

From Abraham: A chemist has one solution that is 35% pure acid and another solution that is 75% pure acid. How many cubic centimeters of each solution must be used to produce 80 cubic centimeters of solution that is 50% acid? Answered by Penny Nom. 





Three word problems 
20040912 

From Adrian: 1. Increasing area
of a field: Julia's soybean field is 3m longer than it is wide. To
increase her production, she plans to increase her to increase both the
length and width by 2m. If the new field is 46m2(2nd power) larger
than the old field, then what are the dimensions of the old field?
2. Width of a Football Field: If the perimeter of a football
field in the NFL including the end zones is 1040 ft and the field is
120 yd long, then what is the width of the field in feet?
3. Fencing dog pens Clint is constructing two adjacent rectangular
dog pens. Each pen will be three times as long as it is wide, and the
pens will share a common long side. If Clint has 65 ft of fencing, what
are the dimensions of each pen? Answered by Penny Nom. 





A travelling salesman 
20040909 

From Liz: A salesman traveled due west from city A to city B. The distance he traveled, that is the ditance from A to B, was X miles. He returned from B to A and found that he had traveled half the distance, X/2 miles. How can that be? Answered by Chris Fisher and Penny Nom. 





Crossing a river 
20040909 

From Barb: Nine men and two boys, trekking through the jungle, need to cross a river. They have a small inflatable boat and it's easy enough to row it across the river. The boat, however, can hold no more than one man or the two boys. How can they all get across? (Hint. suppose there was only one man and two boys) Does it make math sense and what would the answer be Answered by Penny Nom and Claude Tardif. 





Word problems 
20040519 

From A student: why can't 2nd graders have a easy time doing word problems and drawing pictures with it
Answered by Diane Hanson. 





The problem of Apollonius 
20040425 

From Mitja: There are given 2 circles lying one out of another and one point out of both circles. How to construct a circle passing through a given point and internally tangent to one and externally tangent to the other cirlce? Answered by Chris Fisher. 





Red riding hood 
20040214 

From Frank: Red riding hood had a number of jars to take to grandma's house. As she traveled she gave away 1/3 of them to an old lady. Then later As she walked through the forest a wolf stole 1/2 of her remaining jars. When she arrived at grandma's house she gave her 2/3 of the remaining jars. She kept 6 jars for herself. How many jars did she start out with. Answered by Diane Hanson. 





Three numbers are added in pairs 
20040212 

From Jane: When three numbers are added in pairs, the sums of the pairs are 22, 39, and 45. What are the three numbers? Answered by Penny Nom. 





A quadratic word problem 
20040204 

From Carl: A walkway of uniform has 72m2 and surrounds a swimming pool that is 8m wide and 10m long. Find the width of the walkway. Answered by Penny Nom. 





Unusual occurances 
20040108 

From Martin: My wife and I have a question about the probability of something that happened to us a few years ago. So far, no one has been able to give me even an approximate answer. On my 32nd birthday, my wife and I went out to eat at local Japanese hibachi style restaurant. At the restaurant, couples/families are sat together around the hibachi where the cook performs a show. There was a fifteen minute or so wait, so my wife and I sat in the lounge waiting for our name to be called. When they called our names for the reservation, this is what happened. The first group called was the Martin family. Then they called the Francis family. We were the next family to be called, the Ashton family. My full name is Martin Francis Ashton! I think the odds of that happening to someone are very unlikely, but it did, and there is more. Next, we were all sat at the same table in that order, "Martin" family, "Francis" family, then us, the "Ashton" family. Again, it formed my full name! Answered by Penny Nom. 





Laying decorative bricks 
20040107 

From Duk: Loren is laying decorative brick along both edges of the 21meter walkway up to his house. Each brick is 0.26 meters long. He is placing the bricks end to end. How many bricks does he need to do the job? Answered by Penny Nom. 





Diamonds and Pearls 
20031211 

From Lauren: A crown holds a total of 3080 jewels.
It is made up of diamonds and pearls.
There are 10 times as many diamonds as there are pearls.
How many pearls are there? Answered by Penny Nom. 





Mr.Carter is very cautious 
20031126 

From Bob: Mr.Carter is very cautious. He decides to invest in only three stocks: one low stock, one high stock, one medium stock. Given that the expected annual yields are 6% for low stock, 7% for medium stock, and 8% for high stock, he wants his investment in medium stock to be half of his total investment in low and high stock. How much should I invest in each type fo stocks to expect a total annual return fo $650 form my investments? Answered by Harley Weston. 





Mixing Brazil nuts and cashews 
20031109 

From Bob: Cashews are sold for 1.20 per 1/4 pound and Brazil nuts are sold for $1.50 per 1/4 pound. If you mix 20lbs of Brazil nuts, how many cahsews would it take to make a mix that sells for $1.30 per 1/4 pound? Answered by Penny Nom. 





A worm on a hill 
20030821 

From Lisa and Samantha: A WORM IS AT THE BOTTOM OF A 10 FOOT HILL. HE CRAWLS UP THE HILL 4 1/2 FEET A DAY. AT NIGHT WHEN HE REST HE SLIDES DOWN 2 1/2. HOW LONG DOES IT TAKE THE WORM TO CRAWL UP THE HILL. Answered by Penny Nom. 





Cathy's Clothing 
20030715 

From Cathy: I am supposed to write a practical and useful word problem that would use the following algebriac inequality to solve it: 12x + 25 > 15x + 10. State the quanity that represents x and solve the inequality. Answered by Penny Nom. 





A problem with lugs 
20030711 

From Lori: A young man's car developed a flat tire as he was driving along a deserted street. He pulled over to the curb and did all the usual things: removed the hub cap, unscrewed the lugs and rested them carefully in the hub cap, jacked up the car. As he was putting the spare tire onto the axle he accidentally kicked the hub cap. The lugs rolled out, and all five of them fell down a nearby grate. Peering through the bars of the grate the man thought that he could see the lugs about 6 feet below in a shallow water puddle. He had a problem. How do you think he solved it? Answered by Penny Nom. 





A mixture problem 
20030710 

From A student: Having a problem with word problems. example A chemist mixes a 10% acid solution with a 50% acid solution to form 400mL of a 40% solution. How much of each solution should be used. Answered by Penny Nom. 





A wooden deck around a pool 
20030709 

From Dat: A pond is enclosed by a wooden deck that is 3 feet wide. The fence surrounding the deck is 100 feet long.  If the pond is square, what are its dimensions?
 If the pond is rectangular and the length of the is three times its width, what are the dimensions of the pond?
 If the pond is circular, what is the diameter of the pond?
 Which pond has the most area?
Answered by Penny Nom. 





C is 10 more then the square of... 
20030703 

From Carolina:
C is 10 more then the square of the quotient of the sum of x and y , and the product of x and y. Which equation expresses this relationship?
A. C=(x+y +10)^2 ___ xy
B. C=(x+y)^2 + 10 ___ xy
C. C=(xy)^2+10 ___ x+y
D. C=(x+y)^2 + 10 ___ xy
Answered by Penny Nom. 





Setting up a word problem 
20030630 

From Christie: A rectangular corral is forty feet longer than it is wide. If the perimeter is 220 feet, determine the length and width of the corral. Answered by Penny Nom. 





Sesame Street on Stage 
20030625 

From Christie: Sesame Street on Stage has different ticket prices for adults and for children under 6. Beth and her two children, ages 3 and 4, paid $15 to gain entrance, while Jamie and John Jacobs and their 2year old daughter got in for $19.50. What is the ticket price for adults? Answered by Penny Nom. 





Spacing the spindles for a railing 
20030606 

From Jennifer:
Scott is a homebuilder. He builds railings in which he places spindles. Spindles ar evertical posts taht are equally spaced beneath a horizontal bar. Scott would like a mathematical model to help him determine the amount of space to put between each spindle. The railing must follow the following criteria: The spaces between each spindle must be equal except for the ones at either end. Theses spaces are smaller. They are half the width of a spindle less than the other spaces. The number of spindles needs to be minimized since spindles are costly. Help Scott determine what width of space to use between the spindles. Create a mathematical model to determine the width of space between each spindle in termso f the number of spindles. Use an 8' (96") railing that has 2 1/2" wide spindles. Explain your thinking. For safety reasons the maximum width of a space is 4" Generalize you model to determine the width of spaces for total railing of length L and spindle width s Answered by Penny Nom. 





George and his goat herd 
20030527 

From A student:
George the bulgarian goatherd drives his father's goats into a valley each morning and lets them browse there all day before driving them home in the evening. he notices that each morning the goats immediately separate into groups and begin to feed the number and sizes of the initial groups vary some days there are nine and so days there are three or fewer. there can be groups of one or the whole group. about every five minites one goat breaks away from each feeding group and these breakaway goats form into a new group. George has noticed that by the afternoon, even though the goats continue their regrouping the sizes of the groups have stabilised, and there is always seven feeding groups. How many goats are there in the herd? What are the sizes of the feeding groups once they have stabilised? Answered by Penny Nom. 





The square of my age was the same as the year 
20030414 

From Pat: Augustus de Morgan wrote in 1864, "At some point in my life, the square of my age was the same as the year." When was he born? Answered by Penny Nom. 





A handshake problem 
20030331 

From Jaylan: Suppose you and your partner attend a party with n other couples. Several handshakes took place. No one shook hands with himself (or herself) or with their partner, and no one shook hands with the same person more than once. After all the handshaking was completed, suppose you asked each person, including your partner, how many hands they had shaken. Each person gave a different answer.
Determine how many hands did you shake and how many hands did your partner shake when n=5 Answered by Penny Nom. 





Quadratic word problems 
20030330 

From A student: Question: i think i know the basics of how to solve direct quadratic equations,but how do i go about solving those word problems? i have tried them times and again, but nothing seems to work at all!they are driving me crazy! pls help!:):):):):)  bob & nick earned $1260 each. bob's hourly wage is $3 more than nick's hourly wage. he worked 2h less compared to nick. find the number of hours nick worked.
 there are 2 tanks in henry's house. in tank A, the fish are all goldfish. they are bought at a total cost of $259. in tank B, there are only guppies. the guppies were bought at a cost of $1.20 each. a day later,henry bought 3 more goldfish and put them into tank A. the number of guppies in tank B is now twice the number of goldfish in tank A.the total cost of all the fish that henry has presently,i.e. goldfish & guppies, is $355.30. given that the cost of each goldfish is the same,
a)find the initial number of goldfish in tank A b)find the total cost of all the guppies.  a particular disc can be made to rotate at 2 different speeds. if it is made to rotate slower by 135 revolutions per hour, it wld require an additional 2.7 hour to make 315 revolutions. find the higher speed at which it can operate.
Answered by Penny Nom. 





Sasha's candies 
20030218 

From Pat: Ticktactoe
Sasha and Trudy are playing ticktactoe. Sasha agrees to give trudy two pieces of candy for each game Sasha loses, and Trudy agrees to give Sasha three pieces of candy for each game that Trudy loses. After playing thirty games, Sasha has the amount of candy that he started with. If no ties occurred, how many games did Sasha win? Answered by Paul Betts. 





Storyteller figurines 
20030210 

From A student: It takes 3/4 of an hour to bake a storyteller figurine. If only one figurine can be baked at a time, how many can be baked in 6 hours? Answered by Penny Nom. 





A train with 2 cars 
20030204 

From Michael: A train with 2 cars is traveling at a speed of 80 km/hr from town X to town y, located 800 km from each other. At the same moment that the train departed, a passenger started to walk back and forth from one end of car B to the other at a speed of 100cm/sec. Arriving in town Y, the passenger had already gone and returned 720 times. The length of car A is that of car B plus one fourth of the length of the locomotive, and the length of the locomotive equals the length of Car A plus one fifth of the length of car B. What is the total length of the train? Answered by Penny Nom. 





Problem solving 
20030203 

From Brigitte: My daughter is having lot's of problem with problem solving she is in grade 6. she is using mathematics in action from macmillan/ mcgraw hill. Do you know of any way she can get help, and if there is any tests on line Answered by Diane Hanson. 





Fibonacci exam 
20030128 

From Mike:
My son will be participating in the national math contest. He is a grade 4 student but will be writing the Fibonacci exam for grade 5. He has been given last years exam for practice. Parents have been ask to assist for this part. I was therfore hoping for a little "inside" help on several questions with answers & short explanations. This with a would be greatly appreciated.(from last years exam)  With 3 weights, Mathusalem can weigh any object that has a weight which is smaller or equal to 13 kg, but that weighs a whole number of kilograms. He wants to weigh an object of 7 kilograms. To do so, he must place two of the weights on the left side of the scale, and the third one on the right side. Which one will he have to place on the right side
a)4 b)3 c)6 d)2 e)5  Mathilda uses a rectangular prisms to build stairs. The cross section of each prism is a square which has a side of 1 dm. Mathilda has already put in place 4 steps of a staircase that must have a height of 10 dm. When finished, the staircase will have a volume of 550 dm3. What will the width of the staicase in dm be?
a)10 b)55 c)11 d)1 e)100  The year 1991 was the last palindrome year of the second millennium. The year 2002 is the first palindrome year of the third millennium. Including 2002, how many palindrome years will there be, altogether, in the third millennium ?
a)8 b)2 c)10 d)182 e) 9 Greatly appreciated, Mike
Answered by Penny Nom. 





Some 5th grade problems 
20030124 

From Sabrina:
[What is the greatest common factor of 20,28, and 36?] next problem is [5k+7(k+8)= ] next problem [Curtis simplified 0.8 divided by 0.2 x 0.04 and got 10. Latoya Simplified and got 1.6. is either correct? Can you explaine how you got the answer please.] Answered by Penny Nom. 





Dorothy and the wizard 
20030124 

From Ken:
dorothy was going to see the wizard of oz...she stopped at the bakery and bought a box of cookies. she met the scarecrow and gave him half the cookies. she ate half of the remaining cookies and threw one half cookie away. she met the tin man and gave him half the cookies. she ate half the remaining cookies and threw one half cookie away. she met the lion. she gave him half of her cookies. she ate half the remaining cookies and threw the LAST half cookie away. how many cookies did dorothy leave the bakery with? Answered by Penny Nom. 





The cousin of Sally's sister's boyfriend 
20030123 

From Michael: Sally went to a farm to buy eggs. Returning home, she gave half of them to her sister who, in turn, gave a third of those she had gotten to her boyfriend. The latter, after eating one third of the eggs that he had gotten, gave the rest to his cousin. Given that each egg weighs 70 grams, that Sally cannot carry more than 2.5kg, and that the eggs were raw, calculate how many eggs the cousin of Sally's sister's boyfriend received. Answered by Penny Nom. 





A penny, a nickel, a dime, a quarter, and a loonie 
20030121 

From Blaine: I have 5 coins: a penny, a nickel, a dime, a quarter, and a loonie. How many different amounts of money could I pay using any combination of these coins? Answered by Penny Nom. 





Jo's books 
20030121 

From debra: Jo announces: I have no more than 999 books. Jean says: No Jo, You have fewer than 1,000 books. Mary says: Jo has at least 1 book.
Only one of these statements is true, How many books does Jo own?
I do not know HOW to approach this problem and solve it. Answered by Penny Nom. 





Two numbers have a ratio of 5:3 
20030101 

From Patricia: Two numbers have a ratio of 5:3. The larger number is 36 more than half the difference of the two numbers. What are the two numbers? Answered by Penny Nom. 





The product of two consecutive numbers is 41 more than their sum 
20021115 

From A mother: THE PRODUCT OF TWO CONSECUTIVE NUMBERS IS 41 MORE THAN THE SUM OF THE NUMBERS. WHAT ARE THE NUMBERS? Answered by Penny Nom. 





A pattern in a table 
20021114 

From Thamar: how do you solve for pattern in a table like
the top row is  2  6  12  17  z  the bottom row is  9  13  19  24  blank  question ask in each blank space write a rule to find the next number in the table Answered by Penny Nom. 





Three bags of marbles 
20021108 

From A student: I have 3 bags of marbles 1 bag is labeled blue; 2nd bag is labeled red; 3rd bag is labeled blue & red all the bags are mismarked your job is to take one marble from 1 bag look at it and correctly label all the bags Answered by Penny Nom. 





Mrs. Klein has been losing 1 pound a week for the last year 
20021030 

From Brett: On her diet, Mrs. Klein has been losing 1 pound a week for the last year. Her husband weighs 110 pounds more than she does now. If his weight is twice what her weight was 6 weeks ago, how much does mrs. Klein weigh now? Answered by Penny Nom. 





How many trees were planted in March? 
20021020 

From Allison: The number of trees planted by the Alpine Nursery in April was 3 more than twice the number of trees planted in March. If 71 trees were planted in april, write and solve an equation to find how many trees were planted in March. Answered by Penny Nom. 





At the zoo 
20021020 

From A student: The number of adults at the zoo was 2/9 the number of children. there are 700 more children than adults. The number of men was four times the number of women. The number of girls was four times the number of boys. Find the total nymber of men and boys at the zoo. Answered by Penny Nom. 





Two problems 
20021014 

From Seçkin: i am from turkey i am a teacher in a collage i have two difficult question which i havent solve yet these are very important for me.... Answered by Claude Tardif. 





Nixon, Jefferson, and Madison 
20021008 

From Lisa: The longestlived US presidents are John Adams(age90), Herbert Hoover (also90), and Harry Truman (88). Behind them are James Madison, Thomas Jefferson, and Richard Nixon. The lattter three men lived a total of 249 years, and their ages at the time of death form consecutive odd integers. For how long did Nixon, Jefferson, and Madison live? Answered by Penny Nom. 





8 squares from 12 sticks 
20021008 

From A student: If you have 12 sticks the same size, how do you make them into 8 squares? Answered by Claude Tardif. 





$100 is split between four guys. 
20021003 

From Stephan: $100 is split between four guys. A,B, C, and D. How much money does if person get if B has four more dollars than A, C has 8 more dollars than B, and D has twice as much money as C? Answered by Penny Nom. 





A max/min problem 
20020921 

From Evelina: A window is the shape of a rectangle with an equilateral triangle on top. The perimeter of the window is 300 cm. Find the width that will let the maximum light to enter. Answered by Penny Nom. 





How long will it be before you reach your friend? 
20020916 

From Margaret: Your friend runs at 8 miles per hour and you drive at 40 miles per hour, hence the diatance between you is decreasing at 32 miles per hour. You firend left 2 hours before you so how far has he gone in that 2 hours? How long will it take for the distance between you to decrease to 0 miles if the distance is decreasing at 32 miles per hour? Answered by Penny Nom. 





Formulating equtions 
20020914 

From Theresa: Hello. In math class we have to formulate equations for certin questions for extra credit. We are allowed to ask anyone and anyone can do it for us and explain it to us. Could you please do that? Here are the questions  Jordan has 3 times as much money as Reva. Together they have $44. How much money does each have?
 The Tigers played 48 games. They won twice as many as they lost. How many did they win?
 There are 900 students in Sewickley Academy. There are 20 more girls than boys. How many girls are there?
 A board 400 cm long is cut into 2 pieces. One piece is 66 cm longer than the other. Find the lenght of the shorter piece.
Answered by Penny Nom. 





Mixing solutions 
20020913 

From Margaret: In a chemistry laboratory the concentration of one solution is 10% hydrocholoric acid (HCl) and that of a second soulution is 60% HCl. How many mL of each should be mixed to obtain 50 mL of a 30% HCl solution?? Answered by Penny Nom. 





A fish weighs 10 pounds more than half its weight. 
20020910 

From Rebecca: A fish weighs 10 pounds more than half its weight. How much does it weigh? Answered by Penny Nom. 





I am a 3 digit number. 
20020906 

From Jasmine: I am a 3 digit number. My last digit is 3 times my first digit. My firat digit is twice my middle digit. What numbers am I? There are at least 2 correct answers? Answered by Paul Betts. 





Dan is 4 inches taller than Mike. 
20020904 

From A parent: Dan is 4 inches taller than Mike. Together they are 8 feet 8 inches tall. How tall is each boy in feet and inches. Answered by Penny Nom. 





A square of tiles 
20020830 

From Rosa: How do I go about finding a formula for the number of tiles I would need to add to an arbitrary square to get to the next sized square? Answered by Penny Nom. 





20 men dig 40 holes in 60 days 
20020724 

From Lindsey: 20 men dig 40 holes in 60 days. So, 10 men can dig 10 holes in how many days? Answered by Penny Nom. 





As much greater than 47 as it is less than 105 
20020723 

From Joe: To find the number in question you need to find the number exactly halfway between 47 and 105. Another way of thinking about the number that is halfway between two other numbers is as the average of the two numbers given. Answered by Leenaan Boehm. 





The Praxis II test 
20020709 

From A student: I am taking the Praxis II test and I can't seem to answer certain styles of questions. Please help!!!!!!  In a class of 29 children, each of 20 children has a dog and each of 15 has a cat. How many of the children have both a dog and a cat?
 If there are exactly 5 times as many children as adults at a show, which of the following CANNOT be the number of people at the show? a. 102 b. 80 c. 36 d. 30
 In order to estimate the population of snails in a certain woodland, a biologist captured and marked 84 snails there were then released back into the woodland. Fifteen days later the biologist captured 90 snails from the woodland, 12 of which bore the markings of the previously captured snails. If all of the marked snails were still active in the woodland when the second group of snails were captured, what should the biologist estimate the snail population to be based on the probabilities suggested by this experiment? a. 630 b. 1,010 c. 1040 d. 1080.
Answered by Paul Betts. 





Jack and Jill wrote letters 
20020619 

From Angel: jack and jill each bought a stationary # of sheets of paper in each box were the same # of envelopes were the same jill wrote letters consisting of 3 pages jack wrote letters consisting of 1 page
when they wrote all letters jill had 50 envelopes left and jack had 50 sheets of paper left how many pieces of paper and how many envelopes? Answered by Leeanne Boehm. 





The sum of the areas of two regular decagons 
20020527 

From A parent: The sum of the areas of two regular decagons is 39 square inches, and their radii are in the ratio of 2:3. Find the area of the larger decagon. Answered by Paul Betts. 





Flying with the wind 
20020519 

From SaraJean: It takes 6 hours for a plane to travel 720 km with a tail wind and 8 hours to make the return trip with a head wind. Find the air speed of the plane and the speed of the wind current. Answered by Penny Nom. 





Trains and cracker boxes 
20020429 

From Lindsay: 1)Two trains are 250 miles apart on the same track heading towards eaxh other at 7AM The first train travels at 55mph, the second at 75mph. At what time would they crash? 2)A cracker box measures 12 by 2 by 18 inches. The company wants to double the amount of crackers, but keep the shapes the same[similar] Find the new length[nearest tenth of an inch] Answered by Penny Nom. 





A test drive 
20020423 

From Jennie: At 9 A.M. a test car driving at a constant speed passes a marker 50 miles from it's starting point. At noon the car is about 130 miles from the marker. If the test drive ends at 1:30 P.M., how far will the car be from its starting point? Answered by Penny Nom. 





Problem solving 
20020420 

From Kathy:
 Zachary wanted to run the shoreto shore marathon next month, a 26 mile race from one side of the island where he lived to the other. He decided to work up to 26 miles by running five days a week for the next five weeks. Each day he'd run one mile longer than he did the day before, except for the first day of the week, when he'd run the same number of miles he ran on the last day of the previous week. He wanted his last two practice runs to be 26 and 27 miles long.
How many miles would he have to run on his first practice run?
 A school just bought a new set of encyclopedias. The front and back covers are 1/8 inch thick, and the pages are 1/100 inch thick (in other words, there are 100 pages per inch). the 26 volume set has a total of 5,250 pages. If you assume there is no extra space left between books, then .........
What length of bookshelf will the encyclopedias take up? Answered by Penny Nom. 





The Proof in the Pudding 
20020409 

From A student: The host at a party turned to a guest and said, "I have three daughters and I will tell you how old they are. The product of their ages is 72. The sum of their ages is my house number. How old is each?" The guest rushed to the door, looked at the house number, and informed the host that he needed more information. The host then added, "The oldest likes strawberry pudding." The guest then announced the ages of the three girls. What are the ages of the three daughters? Answered by Claude Tardif. 





Meg's biscuits 
20020329 

From Tami: Meg's biscuits recipe calls for 4 cups of flour for every 1.5 cups of milk. If Meg uses 6 cups of flour, how many cups of milk will she need? Answered by Penny Nom. 





A hamburger and a soft drink 
20020323 

From A student: A GROUP OF FRIENDS WENT OUT TO LUNCH. EACH BROUGHT A HAMBURGER AND A SOFT DRINK. TOGETHER A HAMBURGER AND A SOFT DRINK COST MORE THAN A DOLLAR. THE TOTAL COST FOR THE GROUP WAS $17.81. THERE WAS NO TAX OR TIP INCLUDED. IF A HAMBUGER COSTS 2 CENT MORE THAN TWICE A SODA, FIND THE COST OF THE HAMBURGER. Answered by Leeanne Boehm. 





How much olive oil? 
20020315 

From Annie: Joe used 1/3 cup of olive oil, which was 3/4 of the amount that he had. How much olive oil did he have! Answered by Penny Nom. 





What number am I? 
20020303 

From Samantha: I am an even number that has more ones than tens. My thousands digit is the quotient of 9 divided by 3 and my tens digit is the sum of 3 and 3. I have no hundreds. What number am I?......Please answer this for me...The answer I come up with is 3,060...Is this right?.. Answered by Penny Nom. 





Alfredos house number 
20020221 

From Aunt Patty: Alfredos house number is between 20 and 35. The sum of the digits is less than 5. If you subtract 1 from it you would get a multiple of 3. If you add three, you get a multiple of 5. What is Alfredos house number. Answered by Penny Nom. 





Shipping charges 
20020219 

From Sohail: A mail order company charges a fixed fee for shipping merchandise that weighs 1 pound or less, plus an additional fee for each pound over 1 pound. If there shipping charge for 5 pounds is $4.80, and for 12 pounds is $6.20, find the fixed fee and the additional fee. Answered by Penny Nom. 





A farmer takes 100 animals to the market to sell. 
20020219 

From Ann: A farmer takes 100 animals to the market to sell. All are sold and $100 is earned. The prices were $5.00 per cow, $1.00 per sheep and $.05 per pig. At least one of each kind of animal was sold. How many of each kind of animal did the farmer take to market? Answered by Penny Nom. 





A man and his wife walk up a moving escalator 
20020213 

From Monty: A man and his wife walk up a moving escalator. The man walks twice as fast as his wife. When he arrives at the top, he has taken 28 steps. When she arrives at the top, she has taken 21 steps. How many steps are visible in the escalator at any one time. Answered by Peeny Nom and Claude Tardif. 





Baseball and sit ups 
20020131 

From A student: A baseball team won 8 more games than it lost. If it played 56 games, how many games did it win? On the first day of practice, Paul did 3 sit ups. On the second day he did 5, and on the the third day he did 8, and on the fourth day he did 12. If this pattern continued, how many situps did ihe do on the sixth day of practice? Answered by Penny Nom. 





A sale on eggs 
20020117 

From A student: A store had a sale on eggs, selling 13 eggs for the usual price of a dozen eggs. As a result, the price of the eggs was reduced by 4 cents a dozen. What is the original price for a dozen eggs? Answered by Penny Nom. 





The famous "train problem" 
20020112 

From Karen: How do you solve the famous "train problem"? For example, 2 trains leave different stations at the same time. One is traveling at 50 mph and the other at 40 mph. How long does it take them to meet? Answered by Penny Nom. 





Nickles, dimes, quarters and fifty cent pieces 
20020108 

From A parent: The total for all coins counted is $4,564.50 The last coin added to the pile is a 50 cent piece There are 8 times as many 50 cent pieces as there are quarters There are 6 times as many dimes as nickles How many of each are there? Answered by Penny Nom. 





Maple trees and pine trees 
20020106 

From A student: A team of scientists found that in a forest there was four maple trees for every nine pine trees.How many maple were there if they counted 45 more pine than maples? Answered by Penny Nom. 





Feeding Jumbo 
20011221 

From Lupe: There are 2 dogs one named major and the other jumbo. major weighs 100 pounds and jumbo 150 pounds. they eat dry dog food which comes in a 40pound bag that cost $30. Together, major and jumbo eat a whole bag a week. major eats two fifths of the bag while jumbo eats the rest.How much would it cost to feed jumbo in february, which has 28 days? Answered by Penny Nom. 





Making toys 
20011217 

From Karen: Jonathan and Morgan are two of Santa's elves. Jonathan can make a toy in eleven hours. Morgan can make the same toy in nine hours. How long it take for both Jonathan and Morgan to make the toy if they were working together? Answered by Claude Tardif. 





A 1 m by 1 m square box in the xyplane 
20011215 

From Murray: Inside a 1 m by 1 m square box in the xyplane, there are finitely many line segments, whose lengths sum to exactly 10 m. Show that there exists a straight line in the plane which crosses at least six of these line segments. (Hint: first, show that there exists a straight line in the plane which crosses at least five of these line segments.) Answered by Claude Tardif. 





Painting walls 
20011212 

From Rizwan: 3 sixth graders painted 4 walls in 3.5hrs. At that rate, how many walls would they paint in 7 hrs. Answered by Penny Nom. 





Renee, Paulo and Peter 
20011118 

From Sue: Renee is 5 years older than Paulo. she is also 7 years older than Peter. The sum of their ages is 21. How old is each person. Answered by Penny Nom. 





what number doubled plus 20 will give you 4/3 the original number 
20011115 

From Hank: what number doubled plus 20 will give you 4/3 the original number
2 x__ + 20 = 4/3 of the original number Answered by Penny Nom. 





A circle and triangle overlap 
20011109 

From Tara: A circle and triangle overlap as shown.the area of the circle is three times the area of the triangle.If the common region is removed,then the area of the rest of the circle would be 14 sq cm more than the area of the rest of the triangle.How many sq cm are in the area of the complete triangle. Answered by Penny Nom. 





Three problems 
20011028 

From Brenda:
 Joseph is planting bushes around the perimeter of his lawn. If the bushes must be planted 4 feet apart and Joseph's lawn is 64 feet wide and 124 feet long, how many bushes will Joseph need to purchase?
 The cost of a long distance phone call is $1.50 for the first two minutes and $0.60 for each additional minute. How much will Maria pay for a 24 minute phone call?
 Find the next three numbers in the pattern. 1,3,7,15,31,___,____,___.
Answered by Penny Nom. 





Who owns what pet? 
20011003 

From A parent: Don, Frank, Jenny, and Ken each come from one state, either Alaska, Maine, Montana, or Oklahoma. They each speak one primary language, either English, french, Russian, or Spanish. And they each have one of four pets, a chinchilla, a dog, a hamster, or a turtle. Figure out which language and what pet each of the four people have, using the following clues. . . . Answered by Judi McDonald. 





Joan and Jan work together 
20010926 

From Karyna: Joan and Jan work together and they set up a bandstand in just 24 minutes, but if Joan does it by herself she takes 1 hour. How long would it take Jan to set up the bandstand by himself? Answered by Claude Tardif. 





Bicycles and tricycles 
20010926 

From Sally: A bicycle shop has 5 bicycles and tricycles to repair. They have 12 wheels. What strategy would you use to determine how many bicycles and tricycles need to be repaired? Answered by Claude Tardif, Diane Hanson and Penny Nom. 





Scoring a college placement test 
20010926 

From Carmen: A college placement test consist of 75 multiplechoice questions, each having 5 possible answers. The exam is scored by subtracting from the number of correct answers onequarter of a point for each question answered incorrectly. If a person answers every question on the exam and scored 45, how many questions were answered wrong? Answered by Penny Nom. 





Investing in a yacht 
20010926 

From Junior: Marvin and his four friends wish to invest in a yacht by sharing equally in the cost. As the date of sale approaches, Marvin realizes that if three more people join the partnership, each partner's share would decrease by $18,000. How much does the yacht cost? Answered by Penny Nom. 





Julia goes to work 
20010925 

From Karyna: On one October morning, Julia rides her bike (at 12 miles per hour) from her home to her friend Ida's house; then the two of them walk (at 6 miles per hour) to work. If it takes an hour for Julia to go the 10 miles from her home to work, how far does she walk? Answered by Penny Nom. 





What are the two numbers? 
20010924 

From A student: What are the two numbers.  the sum of two numbers is 15. 6 times the smaller number is 4 times the larger number .find the two numbers.
 the sum of the two numbers is 28. 2 times the larger number is 5 times the smaller number minus 7. find the two numbers.
Answered by Claude Tardif. 





David's wages 
20010924 

From Kimberlee: My math question is David earns $6.00 per hour plus $9.00 for every extra hour he works over 40 hours per week. If David earned $285.00 last week, how many extra hours did he work? Answered by Penny Nom. 





27 
20010910 

From Kacy: In class we were given this problem. We have the numbers 30, 29, 19,11,26. these numbers = 27 in some way but how? the numbers can be applied any way using +  / X ( ) but can only be used 1 time each. can you please help me. Answered by Claude Tardif. 





What did the girls score on average? 
20010720 

From Rajesh: The students of two schools were sitting the same test. The students attending the first school scored 74 on average; within this the average scores of the boys and the girls were 71 and 76, respectively. The corresponding scores in the other school were 84, 81 and 90, respectively. If the average score of all boys was 79, what did the girls score on average? Answered by Penny Nom. 





Geometry problems involving triangles 
20010607 

From Sandi: Find the radius of the largest circle contained in a right triangle whose legs are 8 and 15 and hypotenuse is 17. If the right triangle has legs a and b and hypotenuse c, find an expression for the radius of the circle. Answered by Penny Nom. 





Election in Angletown 
20010607 

From Zoe: At the last school election in Angletown 4620 votes were cast. Candidate Acute received 236 more votes than Candidate Obtuse. Candidate Right received 698 votes more than Candidate Acute. Candidate Straight received 256 votes less than Candidate Right. How many votes did each receive? Answered by Penny Nom. 





A few problems 
20010422 

From Carol: Hello I am a College student trying get through my elmentry concepts class. I am also working with the middle and elementry school student with their work. I was given a few problems to work on and i am having a hard time explaining them to students. DO you think you can help with a coupld of these questions! Answered by Penny Nom. 





The number of occurrences of 0 is __, of 1 is __, of... 
20010417 

From Martyanne: "In this sentence the number of occurrences of 0 is __, of 1 is __, of 2 is __, of 3 is __, of 4 is __, of 5 is __, of 6 is __, if 7 is __, of 8 is __, of 9 is __."
Each blank is to be filled with a numeral of one or more digits, written in decimal notation. Answered by Claude Tardif. 





Parabola problems 
20010410 

From Kathleen:
 Graph each function and state its domain and range. y = 3x^{2} + 4
 For each parabola find: i) the direction of opening
ii) the coordinates of the vertex iii) the yintercept iv) the xintercepts y = x^{2} + 3
 Find the equation of each parabola vertex at (0, 2) and passing through the point (3,7)
Answered by Harley Weston. 





12 RTV's 
20010327 

From Christine:
 In order to promote the 2000 Census and encourage participation, 12 Road Tour Vehicles(RTV's) set out from 12 locations across the US for a 10 week promotion tour last February. The RTV's reportedly traveled a total combined distance of 97,911 miles. What was the aberage number of miles traveled in a day by each RTV?
 2. The 12 RTV's mentioned above traveled a total combined distance equivalent to traveling 12.35 times around the earth at the equator. To the closest mile, what is the radius of the earth? Use 3.14 as your approximation for pi.
Answered by Leeanne Boehm. 





problem of the week 
20010306 

From Peggy Allan: My son has been challenged with "the problem of the week" and I am unable to assist him in finding a reasonable solution. Problem 1, Julio needs to draw a line segment 15cm long. He does not have a ruler. He does have some sheets of letter size paper 28 X 21.5 cm. Describe how Julio can use the paper to measur 15 cm. Answered by Claude Tardif. 





P vs NP problem 
20010301 

From Roy: What math journals would publish a proposed solution to the P vs NP problem when the work has been done by an amateur mathematician who has no degree in math? Answered by Claude Tardif. 





Books and cars 
20010213 

From Aquilya:
 A pile of books is 96.08cm. If each book is 0.8cm thick. How many books are in th pile?
 2. A car travels 9.84km on 0.6 litres of petrol. How far will the car travel on 3.7 litres of petrol?
Answered by Penny Nom. 





A dog and a rabbit 
20010209 

From Josh:
1. A dog and a rabbit are 160 meters a part for every 9 meters that the dog runs , the rabbit jumps 7 meters. How many meters must the dog run in order to vertake the rabbit??? 2. A cars odometer reads 15951 KM. Find the least number of kilomaters to travel until the palindromic number appears??? Answered by Leeanne Boehm. 





Bicycles and phone calls 
20010208 

From Sarah:
 A bicycle has a diameter of 66 centimeters. How many times must the tire rotate to travel 1 kilometer?explain answer.
 Becky want to make a long distance call to her friend Sarah from a pay telephone.She has $5.00 in change.The call costs $0.90 for the first three minutes and $0.24 for each additional minute.How long can Becky talk to Sarah?
Answered by Leeanne Boehm. 





Buckets of golf balls 
20010208 

From A student: A bucket containing 40 golf balls weighs 135 ounces. The same bucket with 20 golf balls weighs 75 ounces. What is the weight of the bucket? Answered by Claude Tardif. 





Crossing the dessert 
20010129 

From Zach: An Explorer needed to make a 5 day trip across a dessert. Each man with him could carry exactly 3 days food and water. For one man how many men will it take to cross the dessert? Answered by Claude Tardif. 





Some algebra 
20010123 

From Thomas: If a is 4 more than the quotient of b and 3, and if b=2, then what is the value of a? Answered by Penny Nom. 





8, 4, 2, 18, 1, 9 
20010111 

From Neyra: Place each number below in one of the blanks to create the most meaningful and realistic story possible. Answered by Claude Tardif. 





Derfs, Enajs and Sivads 
20010107 

From John and Norman: All Derfs are Enajs. Onethird of all Enajs are Derfs. Half of all Sivads are Enajs. One Sivad is a Derf. Eight Sivads are Enajs. The number of Enajs is 90. How many Enajs are neither Derf nor Sivad? Answered by Penny Nom. 





Developing a community garden 
20001026 

From adam: Robin's class is developing a community garden. There are 15 students in Robin's class. They volunteer to work in a community garden at various times during the school week. Robin's teacher says it will take about 3 weeks to complete the project if 3 students work 1 hour each day. Some students can work on more than one day. The following table lists the number of students who can work on various days. . . . Answered by Penny Nom. 





Cutting the lawn 
20001026 

From Kacie: Ellen can mow a lawn in 2 hours. Mary can mow the same lawn in 1.5 hours. How long would it take them to mow the lawn together? Answered by Penny Nom. 





Working together on a job 
20001023 

From Nicole: WORKING TOGETHER ON A JOB: Patrice, by himself can paint 4 rooms in 10 hours. If he hires April to help they can do the same job together in 6 hours. If he lets April work alone , how long will it take her to paint 4 rooms? Answered by Claude Tardif. 





Tapes and CD's 
20001022 

From Arnold: Nicole has 25 CDs and tapes altogether. When she tries to pair them up, she has 4 CDs left over. How many tapes does Nicole have? Answered by Penny Nom. 





The perimeter of a football field 
20001018 

From Paige: The width of a football field is 67ft greater than the length. The perimeter is 480ft What is the width and length? Answered by Penny Nom. 





Transporting bananas 
20001018 

From Krystie: A farm has 45 bananas, a man has to take a truck and transport 15 bananas to a market that is 15 miles away. Every mile he travels, he must eat a banana. I have to get at least one banana to the market Answered by Penny Nom. 





Cutting the cake 
20001005 

From Cherie: How can you divide a cake (circle) into 14 pieces by using only 4 straight lines? Answered by Penny Nom. 





Selling chickens 
20000912 

From Rick: A man raised chickens. He sold all but 8 of them. The first buyer bought 1/3 of all the chickens + 2/3 of a single chicken. The second buyer bought 1/3 of the remaining chickens + 1/3 of a single chicken. The third buyer bought 1/3 of the remainder + 2/3 of a chicken. How many chickens did the seller own before selling any? All chickens were alive and whole when the buyers received them. Answered by Penny Nom. 





Making milkshakes 
20000904 

From Linda: To make a chocolate milkshake, 3 parts chocolate syrup are mixed with 2 parts malt. To make a vanilla milkshake, 2 parts vanilla syrup are mixed with 1 part malt. If equal parts chocolate and vanilla milkshakes are mixed, what is the proportion of malt to milkshake? Answered by Penny Nom. 





A number problem 
20000902 

From Lalita Balu: Can you arrange 1234567890 to add up to 100? Answered by Penny Nom. 





Adriana's earnings 
20000828 

From Adriana: On Friday Adriana earns half as much as she did on Thursday. On Saturday she earns twice as much as she did on Thursday, if her total for 3 days is $63.00 how much did she earn each day? Answered by Penny Nom. 





Three pattern questions 
20000822 

From Michael Rodriguez: I have 3 pattern questions that I need help answering, please.  6 and 7 = 42
2 and 5 = 10 4 and 8 = 8 5 and 9 = ?  7 and 5 = 1
9 and 12 = 3 10 and 15 = 5 12 and 16 = ?  1st = 1
3rd = DEF 10th = * 6th = ? Answered by Claude Tardif. 





Six typists 
20000819 

From Paula Duncan: If it takes a typist 4.5 hours to type 860 words, how many hours would it take 6 typist to do 16800 words? Answered by Penny Nom. 





Three consecutive odd integers 
20000818 

From Wallace: A sixdigit integer XYXYXY, where X and Y are digits is equal to five times the product of three consecutive odd integers. Determine these three odd integers. Answered by Paul Betts. 





Two word problems 
20000816 

From Bridget: A whale's head is 72 inches long... its tail is as long as its head plus half the length of its body, and its body is half the entire length. How long is the whale? Also, An author published a book every two years. When the seventh one was published, the sum of the years of publication was 13,804. In what year was the author forst published? Answered by Penny Nom. 





Rectangles and algebra 
20000613 

From Kirstin: A rectangle's length is 4 more than twice its width. The area of the rectangle is 336m squared. What is its length? Answered by Paul Betts and Penny Nom. 





Problems 
20000606 

From Debbie Cummins: I am a Mum of a 12 yr.boy needing help with some math problems. I need not only the answers but how it is worked out.  Both the leftmost digit & the rightmost digit of a 4 digit number N are equal to 1. When these digits are removed, the 2 digit number thus obtained is N div by 21 Find N.
 Find all 3 digit even numbers N such that 693xN is a perfect square, that is, 693x N = k x k where k is an integer.
. . . Answered by Paul Betts and Claude Tardif. 





4 Color map Theorem 
20000602 

From Rick Slen: I am challenging my students to find a map that can not be coloured using only 4 colours. I know that it is not possible, but one boy drew a map with a "country" totally surrounding all the others so of course it touched all other colours. How do I explain that this type of map is not permissable? Answered by Denis Hanson. 





The Village of Truth 
20000510 

From Sean Pearson: Our teacher gave us a logic problem involving two villages: the village of truth, and the village of lies. The problem is in asking two guards the right question to gain entrance to the fenced compound the villages are in without being shot. Have you heard of this problem ? Answered by Harley Weston. 





Running Through a Train Tunnel 
20000401 

From Eugene Chan: A man is running through a train tunnel. When he is 2/3 of the way through, he hears a train that is approaching the tunnel from behind him at a speed of 60 mph. Whether he runs ahead or back, he will reach an end of the tunnel at the same time the train reaches that end. At what rate, in miles per hour, is he running? (Assume he runs at a constant rate.) I think the answer (12 mph) is wrong. Also, I believe it should read 1/3 of the way through, but don't know how to prove it. Could you come up with some way to prove it, please? I would really appreciate it. Answered by Penny Nom. 





Word problems 
20000331 

From Amy: Question:  a north bound train left at noon. four hours later a south bound train left the same station. at 5 o'clook they were 160 miles apart. what was the rate of both if the north bound train was going 20 miles faster than the other one.
 clark's final exam was given 5 times the weight of the weight of a weekly test. the avgerage of 15 weekly test was 91. the overall weighted average was 85. what did he make on the final.
Answered by Penny Nom. 





Making fruit salad 
20000329 

From A grade 5 student: Miss.Muffet males a fruit salad by adding 31/2 pounds of grapes and 4 1/4 pounds of apples to every 2 1/4 pounds of melon. How many pounds of grapes does she use in 50 pounds of fruit salad? Answered by Claude Tardif. 





Sylvester's Problem 
20000323 

From Sheryl Webb: I am trying to find a proof of the theorem: Given n points in a plane, there is a line that contains exactly two points. Answered by Chris Fisher. 





The Kennedy Pep Club 
20000317 

From David Grimmer: The Kennedy Pep Club rented a bus to take all of its members to a baseball game. The cost per person was to be $18.00. However, those making the trip had to pay $24.00 each because 10 members cancelled at the last minute. How many pep club members took the bus to the game? Answered by Penny Nom. 





Two problems 
20000314 

From Teresa Bostic :
 A man's age at death was 1/29 of the year of his birth. How old was he in 1949?
 At a contest, 2 persons were asked their ages. Then to test their ability mathematically, they were asked to give the ages together. One gave 44 and the other gave 1280. The first had subtracted one age from another, and the second had multiplied the two together. What were their ages?
Answered by Penny Nom. 





An integer maxmin problem 
20000313 

From Paul Servic: Maximize Q = xy^{ 2} where x and y are positive integers such that x + y^{ 2} = 4 Answered by Penny Nom. 





A goat problem 
20000310 

From Nancy: A farmer has a fencedin, circular field with an area of about one acre. A goat in the field is tethered to one of the fence posts with a rope which gives the goat approximately onehalf acre of grazing area. To the nearest foot, how long is the rope? Answered by Chris Fisher. 





The isoperimetric theorem 
20000224 

From Raj Bobal: How can you prove Mathematically that the maximum area enclosed by a given length is a circle? Answered by Chris Fisher. 





Jogging up a hill 
20000217 

From Aaron Williams: A man jogs down the hill at 6 miles per hour and back up at 4 miles per hour. The total time that he travels is 5/4 hours. What is the total distance that he jogged. The solution is supposedely 3 miles, but i believe that it is 6. Can you help me? Please. Answered by Claude Tardif. 





Weighing bales 
20000215 

From Thinh Than: You have 5 bales of hay. and they were weighed but they didn't weigh them individually, they were weighed in pairs. The pairs were 1&2, 1&3, 1&4, 1&5, 2&3, 2&4, 2&5, and so on. The weights of the pairs were 80,82,83,84,85,86,87,88,90, and 91. Can you tell me how much the bales weigh individually. Answered by Claude Tardif. 





Tennis doubles 
20000204 

From Brittany Allinson: Cheri, Beth and Jacinta are daughters of Mr. Sullivan, Mr. Marchand, and Mr. Benoit. Four of these people are playing tennis doubles. Mr. Benoit's daughter and Mr. Sullivan are partners. Cheri's father and Mr. Marchand's daughter are also partners. There aren't any father/daughter combinations. Who is Cheri's father? Answered by Penny Nom. 





Filbert Family Circus 
20000204 

From Sarah: As Clyde moves his broom around the circus ring, he thinks that he has finally found a job where he can make a clean sweep of things. Clyde is sweeping the ring where the lions perform in the Filbert Family Circus. The ring is 76 feet across and Clyde is using a broom 3 feet wide. He starts at the outside edge and works his way to the middle, making circles around the ring. After sweeping 3/4 of the ring, Clyde sees the lions coming with their trainer and scurries out of the ring. How many trips around the ring did he make? Answered by Penny Nom. 





100% on two tests 
20000201 

From Craig and Chelsea Bruzzone: A class of 35 students took a math test and a science test. 12 students got 100% on the math test. 9 students got 100% on the science test. There were 19 students who made less than 100% on both tests. How many students made 100% on both tests? Answered by Penny Nom. 





Mark's life 
20000130 

From Jean and Larry Brandemuehl: Mark passed 1/6 of his life in childhood, 1/12 in youth, and 1/7 more as a bachelor. Five years after his marriage, there was born a son who died four years before his father, at half his father's (final) age. How old was Mark when he died? Answered by Penny Nom. 





Can't make an equation! 
20000130 

From Maggie Clarke: An estate is to be distributed among the wife, 3 children and 2 grandchildren. The children will each receive 2x as much as each grandchild, and the wife will receive 4x as much as each child. If the estate amounted to $115,000, how much will each person receive? Answered by Penny Nom. 





Two problems 
20000129 

From D. J. Anthony:
Hi, I am taking a course "math for elementary teachers" and I have two problems.  How thick is a sheet of paper in your textbook.
 A little island has a population of 1,000 people. It doubles every 30 years. What will the population be in 30 years?, in 60 years?, when will it be over one million?
Answered by Peny Nom and Claude Tardif. 





Word problem 
20000124 

From April:
Ok, my algerbra teacher gave me this problem and by just looking at it I can tell what the answer is but he wants me to show how I got the answer in an equation form. The tempature at 7am on a cold day was 4 degrees Celcius. At 3pm the tempature was 1 degree Celcius. Write and solve an equation to find out how many degrees the tempature rose between 7am and and 3pm. Answered by Penny Nom. 





A three digit number 
20000113 

From Manali Shah: My son is in 5th grade, he has a math problem. There is three digit number, which is greater than 500, can be divided by 7,9 and 11, but cannot be divided by 2,4,6, and 5. Answered by Harley Weston. 





How many coins is one calculator? 
20000109 

From Mandy Brockmann: Tom weighed 1 pen and his calculator with 4 coins. Then he weighed his calculator and 3 pens with 12 coins. How many coins is one calculator? Answered by Claude Tardif. 





Passing trains 
19991210 

From Nancy: Two trains, each of 80 cars, must pass on a single track which has a deadend siding. How can they pass if the siding can only hold a locomotive and 40 cars? I do not understand this...help. It will be due monday. I thought it would be simple if the siding could hold 80 cars. Answered by Penny Nom. 





Camels and bananas 
19991202 

From Marie Rich: Corey Camel's harvest, worth its weight in gold, consists of 3000 bananas. The market place where the stash can be cashed in is 1000 miles away. However, Corey must walk to the market, and can only carry up to 1000 bananas at a time. Furthermore, being a camel, Corey eats one banana during each and every mile she walks (so Corey can never walk anywhere without bananas). How many bananas can Corey get to the market? Answered by Claude Tardif. 





Get rich quick 
19991202 

From Holly Hutson: If one cent were placed in an investment that doubles in value every day, what would be the value of the investment at the end of 30 days? Answered by Penny Nom. 





An area problem 
19991129 

From Vicky Birch: The length of a rectangle is three times it's breadth. If the length were 6 meters less, and the breadth were 6 meters more, the rectangle would be a square. Make a mathematical model and solve the resulting equation to find the breadth of the original rectangle. What is the area of the square? Answered by Penny Nom. 





Two candles 
19991124 

From Skip Simpson: You have two candles the same length. They are lit at the same time. One burns down in 4 hours; the other in 5 hours. How long does it take before one candle is three times the length of the other candle? Answered by Walter Whiteley. 





A goofy clock 
19991120 

From Kate: While repairing a watch, a jeweler removed the hands and inadvertently replaced the hour hand on the min. spindle and vice versa. he set the hands to read 2:00pm, which was the correct local time when I picked up the watch. A few minutes later, I noticed that the hands were taking goofy positions. What was the first time thereafter that the watch would show the correct local time? Answered by Chris Fisher. 





A matching quiz 
19991120 

From William J. Ricciardi: I gave a matching quiz the other day and one of my students got all 9 incorrect. That got me thinking......What is the probability that someone could get all 9 questions incorrect? Answered by Peny Nom. 





Selecting some players 
19991120 

From Korbin Brown: Roger Craig, during his term as team manager of the San Francisco Giants, received a strange communication from the team general manager, Al Rosen. Mr. Rosen told him to select 25 players according to this formula: 1/2 of the team had to be outfielders and infielders 1/4 of the team had to be starting pitchers 1/6 of the team had to be relief pitchers 1/8 of the team had to be catchers Roger was a bit confused by Al's request, yet complied anyway. How did he do it? Answered by Claude Tardif. 





The sixth game 
19991116 

From Stephanie Sprunger: Janice scored 18,21,27,16,and 19 points in five basketball games. How many points must she score in the next game to raise her average to 22 points per game? Answered by Penny Nom. 





Working Backwards 
19991016 

From Linda: I am having problems finding examples of problems that require "Working Backwards" used as a strategy for solving. We are required to give a presentation on Monday, October 25, 1999 in our school districts math class. We are trying to become better problem solvers and how to teach problem solving in the elementary classroom. Help! I can't find anything in my web searches. Answered by Penny Nom. 





A donkey and his carrots  part 2 
19991002 

From Sarah Klink and Brenda Gamble: Does anyone know the solution of the donkey who had to carry 3000 carrots to the market which was 1000 miles away? The donkey can only carry 1000 carrots at a time and he eats one carrot every mile he walks but this is only when he is carrying carrots. How many carrots can get to the market with the donkey carrying them? Answered by Claude Tardif. 





Jose and Arthur 
19990926 

From Joel Hammer: Jose can run around the track in 40 seconds. Arthur runs with Jose but in the opposite direction. They meet every 15 second. How long will it take Arthur to make one trip around the track? Answered by Denis Hanson. 





Bob and his dad 
19990914 

From Yvette: "Bobs dad is 27 yrs older then Bob. The sum of their ages 5 yrs ago was 45 yrs. How old is Bob now?" Answered by Penny Nom. 





Bales of hay 
19990913 

From Ivy: You are given 5 bales of hay. Two bales are weighed at a time, which equal the following weights: 110, 112, 113,114,115,116,117,118,120,121. What does each individual bale weigh? Answered by Harley Weston. 





Using Factoring in Problem Solving 
19990909 

From Lori: I have a problem with a problem. The Problem is....The sum of the squares of two consecutive positive even integers is 340. Find the integers. Answered by Penny Nom. 





The three jugs problem 
19990902 

From Kent Lane: I wonder if you could help me figure out this secondary Discrete Math Problem. I cannot figure out where this comes from. Here's the question: You have three containers. Container 1 is a three (3) liter container. Container 2 is a five (5) liter container. Container 3 is an eight (8) liter container that is full of liquid. The goal is to get 4 liters in one of the containers. Stipulations: There are no marks on the containers to measure out the liquid. All you know is that 1 is 3 l., 2 is 5 l., and 3 is 8 l. full of liquid. Answered by Chris Fisher. 





The Bellhop Problem 
19990829 

From Gerard O'Neill: Three fellows going to a Math Conference book into a motel. "That will be $30.00" says the bellhop. Each fellow gives $10.00 and they go off to their room. The manager enters and says "That was a $25.00 room. Go and give them $5.00 back." The bellhop heads off but thinks....."how am I going to split $5.00 between 3 fellows? Hey I will keep two dollars and give each guy a dollar." He does just that.......each fellow now paid $9.00 and the bellhop kept two. 3 X 9= 27 plus the bellhops two = $29.00 Where is the missing dollar? Answered by Harley Weston. 





Crossing the Bridge 
19990827 

From Debbie Walter: If you have four people who need to cross a bridge in the dark with only one flashlight and only two of them can cross at a time and their speeds of crossing are as follows:  one person can cross it in one minute
 one person can cross it in two minutes
 one person can cross it in five minutes
 and the slowest person can cross it in ten minutes
what is the shortest amount of time it would take to get all four across the bridge? Answered by Penny Nom. 





The three cousins 
19990601 

From Irena: I have three cousins on my dad's side. The product of their ages is 84. Next year the youngest will be 1/4 the age of the middle cousin. In 2 years from now, the oldest will be twice the current age of the middle. What is the age of my oldest cousin? Answered by Harley Weston. 





Three Daughters 
19990518 

From Norm Campbell: I recently received a beat up copy of the three daughters question. I have only some of the question. It ends after the statement "the oldest one looks....... It does not finish. Is there any chance that someone can finish it off for me? Answered by Rick Seaman and Harley Weston. 





Missing the boat 
19990511 

From Judith Moe: Our daughter is in Grade 3 and seems stubbornly determined NOT to learn how to add and subtract. She's been assessed as quite intelligent in reading and writing,...Do you know of any alternative approaches to teaching/learning math that are proving useful in such circumstances. Answered by Diane Hanson. 





Bill and Sam at the Casino 
19990423 

From Rham Stewart: Bill and Sam went off to bet at the casino. Each started with the same number of dollars. At the end of the first hour, Bill had won 20$ and sam had lost 20$. At the end of the second hour, BIll had lost two thirds of his money, and Sam had won the same amount that Bill had lost. At that point, sam had four times as much money as BIll. How much did each one start with? Answered by Penny Nom. 





Shopping at Wegman's 
19990422 

From Stan: Joanne, Steve, Pat, Alice, Joan, and Bill go to Wegman's at the same time. Joanne buys 2 gal of milk, 1 dozen oranges, 8 apples, and 2 lb. of ground beef, paying a total of $13.24. Steve buys 3 qts. of milk, 5 lbs. of ground beef, 10 lb. of potatoes, and 2 bags of mixed vegetables, paying a total of $16.95. Pat buys 3 gal. of milk, 2 dozen oranges, 1 dozen apples, 5 lb. of potatoes, and 5 bags of mixed vegetables, paying a total of $25.09. .... Find the cost of: 1 qt. of milk, one orange, one apple one lb. of ground beef, one lb. of potatoes, and one bag of mixed vegetables. Answered by Penny Nom. 





A ladder problem 
19990422 

From Michael Blade: There is a cube box 3feet x 3feet x 3ft resting against a vertical wall on level ground. Resting against the outside corner of the box is a ladder 10 feet tall, this ladder is of course resting on the ground but also against the outside corner of the box and rests on the wall. The question the ladder is divided into two unequal section bounded by the box to the ground and the box to the wall. what are those dimensions? Answered by Penny Nom. 





The birthday problem 
19990419 

From Gordon Cooke: How do I explain the rapid rise in the probability that at least two people in a group of n have the same birthday. We have derived the formula for p(n) and have graphed it and have seen how the results are counterintuitive. At around n=23 p(n)=.5 and at n=50 p(n) is very close to 1. It does not help to simplify the problem (eg use months instead of days) because then our intuition does correspond more closely to reality. Is there some way we can see how the probabiltiy of a "collision" increases with n? It makes me think of data storage problems and hash tables in computer science. Answered by Harley Weston. 





Extra point questions 
19990415 

From W Troy Council: My teacher has given me 5 extra point questions. I have figured out two, but i need a little assistance with 3 others, could you help me with:  A stablehand agreed to work for 1 year. At the end of that time, she was to receive $240 and one horse. After 7 months she quit the job, but still received the horse and $100. What was the value of the horse?
 If the roots of x^{2} + bx + c are pi and square root 2, then find "b" and "c."
 ...
Answered by Penny Nom. 





Two contest problems 
19990414 

From Bruce Baldwin: We have students that are preparing for the Pythagoras Contest which is a nation wide Grade 6 math challenge. In the preparatory tests we have run into several questions that we can not understand. Is there anyone who can help us?  If 1 * 9 = 0, 9 * 8 = 72, 2 * 8 = 9, then 9 * 9 = ?
 ...
Answered by Judi McDonald and Walter Whiteley. 





A word problem 
19990325 

From Anna Gariss: A second number is 4 less than a first number. The product of the second number and 3 more than the first number is 18. Find the pair of numbers. Answered by Jack LeSage and Penny Nom. 





A field trip 
19990318 

From Jennifer Rudd: This word problem is driving me nuts! I could really use your help. Its a secondary level question. Here it is: A group of students planned to charter a bus for a school field trip. Each student was to share the $810 cost equally. However, 3 people were unable to go and this increased the share of each person by $3. How many went on the trip? Thanks! Answered by Jack LeSage and Penny Nom. 





Four Corners Maths Problem 
19990216 

From Helen Williams: I am currently a student teacher in the UK and I have to write a 1000 word report on the following maths problem which I am completely stuck on! PLease HELP!! Choose and 3 by 3 section of the hundred square. Add the total of the four corners. How many different groups of four numbers can you find that add up to that number? eg, Total of 4 corners add up to 48. Adding 2, 13, 22, 11 also make 48 etc.. How many different groups of 4 numbers would add up to 48? How would these results compare with thoses obtained from a 3 by 3 square in which the numbers are consective? eg, PLEASE HELP AS I AM COMPLETELY STUCK? WHY DO ALL THESE DIFFERENT WAYS ADD UP TO THE SAME NUMBER?? Answered by Harley Weston. 





Word problems 
19990209 

From Brian Rodriquez: Please answer these problems with a formula. Also explain in English step by step how these problems should be solved. I know the answer I just don't know how the answer was achieved Thank you very much for trying to help  A ski lift carries a skier up a slope at the rate of 120 feet per minute and he returns from the top to the bottom on a path parallel to the lift at an average rate of 2640 feet per minute. How long is the lift if the round trip traveling time is 20 minutes?
 An airplane on a search mission flies due east from an airport, turns and flies due west back to the airport. The plane cruises at 200 miles per hour when flying east, and 250 miles per hour when flying west. What is the farthest point from the airport the plane can reach if it can remain in the air for 9 hours?
Answered by Jack LeSage and Penny Nom. 





Some Word Problems 
19981217 

From Jennifer Rudd: To Whom It May Concern, I'm having some difficulty with these word problems. Maybe you could help. Thanks.  A matte of uniform width is placed around a painting so that the area of the matted surface is twice the area of the painting. If the outside dimensions of the matte are 40cm and 60cm, find the width of the matte.
 The Joneses start out A 1520km car trip to Walker Park. On the first day they cover 960km. On the second day they complete the trip, but a rainstorm causes them reduce their average speed by 10km/h.If the 2day trip took a total of 20 h, what was the average speed on each day?
 Granny stood up at her grandson's wedding reception and announced " My age now is a perfect square and it is equal to the difference between the square of my grandson's father's age and the square of his mother's age. Come to think of it the difference my age and the square of my grandson's age is seven times the age of his mother, my daughter in law." The grandson's wife remarked to her new husband," That means the difference between the squares of our ages is three times the age of your father!" How old was the bride?
 The volume of a retangular box 4cm high is 144 cubic cm. If the perimeter of the base is 24cm, find the dimensions of the box.
P.S. the first two questions are the most important ones that need to be solved. Thanks for your help!! Answered by Jack LeSage and Penny Nom. 





Problem Solving 
19981015 

From Pamela Fisher: Can you give me a comprehensive list of problem solving stategies. I teach grade one in a K to 8 school and we are working on improving problem solving at all grade levels. I have heard that there is a list of various strategies that we could adapt to different grade levels. Any help you give me would be appreciated. Thank you. Pamela Fisher Answered by Walter Whiteley. 





Students and Lockers 
19981002 

From Mike: There is a row of 1000 lockers. There is a line of 1000 students. Student number 1 starts at the first locker and opens all 1000. Student number 2 starts at the second locker and closes every other one. Student number 3 starts at the third locker and goes to every third one, closing the open ones and opening the closed ones. Student number 4 does the same with every fourth locker and so on down the line... After all 1000 students have gone how many lockers are open and which ones are they? Please help! There is proboly a simple solution but we couldnt figure it out for the life of us. Please let us know how you solve it. Answered by Patrick Maidorn and Penny Nom. 





The Birthday Problem 
19980612 

From Josh Skolnick: if you are at a party what is the least amount of people that have to be there to have at least a 50% chance of having 2 people with the same birthday? and how do you get the answer thank you in advance josh Answered by Harley Weston. 





Logic and Matrix Instruction 
19980424 

From Robin Booker: I need assistance with instruction strategies to teach the construction of a matrix, solving a logic problem. Providing instruction in the construction of a simple matrix , no problem. However, I stumpted on this one. Five players were chosen as All Stars at the basketball banquet. Based on the following clues, find the player's name, team, uniform color and number of points scored.... Answered by Harley Weston. 





Seed Problem 
19980326 

From Jody A. Johnson: Seed Problem: The height of an amazing plant grown from a seed varies linearly with the time it has been in the ground. After six days it is 6cm tall and after 60 days it is 15.8m (1580 cm) tall.  Write the particular equation giving the height as a function of time.
 Find the intercepts and explain them.
 What would be the height in one year?
 How long would it take for the plant to grow to a height of 1km?
I'm having a problem with this equation. Could you please help. Thank you. Answered by Penny Nom. 





Guess and Check 
19971125 

From Don Ramey: Hope you can help !!!! my daughter is in the 4th grade.. she has brought home a homework paper and the subject is problem solving. she does not understand what is expected of her. I have tried to help, but I do not understand either. She is to use the Guess and check Strategy. Ben knows 100 of his neighbors by name. Ten are fish. The rest are frogs and turtles. He knows the names of twice as many turtles as frogs. How many turtles does he know by name.? Please help by explaining the guess and check strategy for a problem like this. Answered by Diane Hanson. 





A donkey and his carrots 
19970128 

From Emily Lind: There is a donkey who carries carrots. A farmer has 3,000 carrots to carry to the market. The market is 1,000 miles away. The donkey can only carry 1,000 carrots at a time and he eats 1 carrot every mile that he walks but this is only when he is carrying carrots. How many carrots can the farmer get to market by having the donkey carrying them? Answered by Penny Nom. 





Smith, Rodriguez and Jones 
19961107 

From Rafayel Ambartsumyan: On a train, Smith, Rodriguez, Jones are the fireman, brakeman, and engineer, but not in that order. Also aboard the train are three businessman who have the same names, a Mr. Smith, a Mr. Rodriguez, and a Mr. Jones. ..... Who is the engineer? Answered by Penny Nom. 





Will this always yield a palindrome? 
19960828 

From Andy Golden: My friend Justin Skywatcher, said that when his children were in 6th grade, they were taught that if you take any number, reverse it and add the two together, a palindrome will result. If not, continue performing the above operations, and a palindrome will eventually result. Will this always yield a palindrome? Answered by Chris Fisher. 





Grade nine problem solving 
19960311 

From Azmat Hussain: Can math problems be actually fun and engaging? Answered by Diane Hanson. 





(5+3)/23= 
20101210 

From chantal: (5+3)/23= Answered by Claude Tardif. 





Qui suisje? 
20070228 

From un parent: bonjour, le problème est le suivant : Qui suisje? Mon tiers augmenté de mes deux cinquième est égal à la moitié de mon triple Serez t'il possible d'avoir la solution à ce problème et que je puisse y comprendre un peu quelque chose quand même Je vous remercie d'avance et espère bientôt vous lire Answered by Claude Tardif. 





Mon problème (né d'un retour aux conclusions du prix Nobel d'économie ) revisité 
20050927 

From Nzitat: Soit L un sensemble de distributions de probabilités. Désignons par p une distribution de probabilité quelconque. En clair p=(p0,..., pm) où m >0 est fini. Appelons Vi, i=1,...,n, une fonction définie sur L et à valeurs dans l'ensemble des réels. De même Wj, j=0,...n est une fonction définie sur L et à valeurs dans l'ensemble des réels. Vi, Wj sont définies ainsi pour tout p:.... Answered by Claude Tardif. 





problème de math 
20050603 

From Nadia: 1* La somme de 3 multiples de 6 consécutifs est 72.Quels sont
ces nombres?
2* Dans la fabrication d’un alliage, on utilise 5g de manganèse
pour 32g de fer.
a) Quelle quantité de manganèse retrouveton dans un morceau
de cet alliage s’il contient 512g de fer? 00015166
b) Quelle est la masse totale de ce morceau si le fer et le manganèse
en sont les seules composantes?
3*... Answered by Claude Tardif. 





J'ai deux fois l'âge que tu avais quand 
20041203 

From Un eleve: Julien dit à Nicolas:"J'ai deux fois l'âge que tu avais quand j'avais l'âge que tu as.Quand tu auras l'âge que j'ai la somme sera égale à 63".A toi de trouver l'âge de Julien et de Nicolas. Answered by Claude Tardif. 





Un problème de math 
20040910 

From Sophie: (V est en fait le signe de la racine carrée)
(3 / V27) x ( V75 ) = ??? Answered by Claude Tardif. 





Un problème mathématique 
20020423 

From Mylène: En me servant de ces chiffres 1 2 3 4 5 6 je dois les utiliser seulement qu'une fois en faisant l'équation suivante.
? X ? X ? __ __ ? ? X ? = 2
Answered by Claude Tardif. 

