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3 consecutive multiples of 11 2017-07-22
From nisha:
using the multiples formula shown at ypur site how can we solve finding 3 consecutive multiples of 11 whose sum is 363
Answered by Penny Nom.
Two consecutive odd integers 2017-07-14
From Adeeb:
Find two consecutive odd positive integers, sum of whose square is 290.
Answered by Penny Nom.
Three consecutive natural numbers 2017-06-11
From Anita:
Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the square of the other two by 60. Find the numbers.
Answered by Penny Nom.
Five consecutive even integers 2016-08-12
From Marcelle:
The average of 5 even consecutive numbers is 112. What is the largest numbers?
Answered by Penny Nom.
Consecutive angles of a parallelogram 2016-01-28
From Hanna:
The consecutive angles of a parallelogram measures
Answered by Penny Nom.
Three consecutive integers 2016-01-07
From ronn:
Three consecutive integers whose sum is 186
Answered by Penny Nom.
Four consecutive integers 2016-01-05
From sherica:
my teacher gave us an assignment and it says here that; THERE ARE FOUR CONSECUTIVE INTEGERS.IF THE SMALLEST ONE IS x ,FIND THE SUM OF THE FOUR INTEGERS. that is the question ...thanks hope that u can answer it
Answered by Penny Nom.
The surface area of a cut pipe 2015-04-27
From ARUN:
dear Sir,

please advise me , how to calculate the surface area of a pipe with diameter of 630 mm and thickness of 67 mm which is cut in a angle of 22.5 degree.

please show me how to calculate the surface area of the pipe which cut in an angle.

Thanking you.

Answered by Harley Weston.
Three consecutive integers 2015-03-28
From Aleksey:
I need help how do I find the second of three consecutive integers if the sum of the first and third is 26?
Answered by Penny Nom.
Two consecutive odd integers 2015-03-09
From gowtham:
The sum of two consecutive odd integers is 20.find the integers
Answered by Penny Nom.
Two consecutive positive integers 2015-03-01
From meha:
Find two consecutive positive integers , sum of whose squares is 365.
Answered by Penny Nom.
Three consecutive odd integers 2014-10-17
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.
Cutting a round cake so that it doesn't dry out 2014-08-26
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.
A word problem with fractions 2014-03-26
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.
Three consecutive whole numbers 2014-03-13
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.
Consecutive Numbers Question 2013-08-11
From Lucy:
Hello,
I have a question about consecutive numbers. So lets say a question tells you to find what three consecutive numbers are that add up to a certain number. To calculate this, would you use 2x+1, 2x+3, 2x+5 or just x, x+2, x+4.
Also, the same question for even numbers. Would you use:
2x, 2x+2, 2x+4 or just x, x+2, x+4.
My math book is confusing because it uses the first strategy(the 2x+…) in some situations and the second strategy(x+…) in other situations. Thus, can you provide me an explanation of why you would use the strategy that is correct?
Specifically, my book answered this question: If “n” is the first of five consecutive odd numbers, what is their average, using n,n+2….=5n+20 and average is n+4(this is the answer),.
For the question: the sum of 4 consecutive odd integers must be:
Divisible by 8 but not necessarily 16(this is the answer), it used the strategy 2k+1, 2k+3…=8k+16.

Thank you so much for taking the time to answer my question.

Answered by Harley Weston.
Three consecutive odd integers 2013-07-08
From sparsh:
Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is:
Answered by Robert Dawson.
Three consecutive numbers 2011-11-29
From Michael:
Find three consecutive numbers such that the second number squared is equal to the first and third added together
Answered by Penny Nom.
Three consecutive terms of an arithmetic sequence 2011-10-30
From Juliette:
Find X when x, 1/2x + 7, 3x -1 are consecutive terms of an arithmetic sequence.
Answered by Penny Nom.
Three consecutive odd integers 2011-10-07
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.
Three consecutive odd numbers 2011-03-11
From George:
Write an equation three consecutive odd numbers whose sum is 75
Answered by Penny Nom.
Three consecutive numbers 2011-01-31
From parth:
name 3 consecutive numbers,each less then a 100,the smallest # is divisible by 6 the next is divisibel by 5 and the largest divisible by 4
Answered by Penny Nom.
Three consecutive odd integers 2010-11-07
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.
Four consecutive integers 2010-10-21
From Mickey:
Find four consecutive integers such that the sum of the first three integers is 20 more then the fourth integer. I know that for consecutive integers the algebraic expression is x+x+1+x+2+x+3
Answered by Penny Nom.
The product of 2 consecutive integers 2010-06-28
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.
The product of two consecutive even integers 2010-05-11
From Terry:
The product of two consecutive even integers is 14 more than their sum. Find the integers.
Answered by Penny Nom.
Consecutive even integers 2010-02-03
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.
A cylinder is cut at an angle of 20 degrees 2010-01-25
From sanjay:
If I have a cylinder with 40mm diameter and I will cut it at an angle 20 degrees so what would be the increased radius or dia.??? of the cylinder
Answered by Penny Nom.
Improper fractions 2010-01-12
From Blanca:
Between which two consecutive natural numbers does the improper fraction 57/56 lie?
Answered by Robert Dawson.
Consecutive odd intergers 2010-01-06
From keyanna:
list five consecutive odd integers, starting with -3
Answered by Robert Dawson.
Cutting a square into four shapes 2010-01-05
From Tracy:
A square with a side of 4 ft needs to be cut into four shapes with the same area. can you find six different was to cut the square?
Answered by Robert Dawson.
Consecutive odd integers 2009-11-09
From Erin:
I'm having trouble with consecutive integers. i know it goes n + n + 1 + n + 2 and so on, but if its odd then do the numbers change to odd ones? i don't know the question is: the sum of four consecutive odd integers is -72. write an equation to model this situation and find the values of the four integers
Answered by Robert Dawson and Penny Nom.
sinA + cosA = 1 2009-11-06
From Nazrul:
What is the solution of sinA+cosA=1 where A is an acute angle? Will A=0 degree be included in the solution? Please explain.
Answered by Harley Weston.
Consecutive positive integers 2009-11-01
From Madi:
I'm doing my homework, and there are questions on Consecutive Positive Integers. I was just wondering, what is a consecutive integer? Or to be more specific, what is a consecutive POSITIVE integer?
Answered by Penny Nom.
Cutting a pipe at an arbitrary angle 2009-10-24
From Carol:
I have read your article on cutting pipe,etc. at a 45 degree angle. I need to develop an equation and pattern for cutting any size pipe (3" to 7") to any degree. I don't understand how to transfer the wave pattern to graph paper.
Thanks.

Answered by Harley Weston.
Four consecutive odd integers 2009-10-24
From Tonya:
the sum of four consecutive odd intergers 2008 what are the intergers
Answered by Penny Nom.
Cubes and squares 2009-09-16
From Stanley:
What is a three consecutive digit number like 5,6,7 , which is two less than a cube and two more than a square?
Answered by Robert Dawson.
Is -100 degree angle an acute angle? 2009-09-02
From Nazrul:
Is -100 degree angle an acute angle? Please explain. Here -100<90.
Answered by Robert Dawson.
Zero Angle 2009-09-01
From Nazrul:
Is zero degree an acute angle? Please explain.
Answered by Janice Cotcher.
Three consecutive odd integers 2009-04-02
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.
Three consecutive odd integers 2009-03-11
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.
The angles of a triangle 2009-03-11
From Marissa:
The angles in a triangle measure 7x-1, 18x+2, and 5x+10. Determine whether the triangle is acute, obtuse, or right. State your reasons clearly.
Answered by Robert Dawson.
wo consecutive numbers with a product of 9506 2009-02-25
From sofie:
find two consecutive numbers with a product of 9506
Answered by Penny Nom.
A railway cut 2009-01-30
From Jean:
A railway cut 200ft. long and 30ft. wide at the bottom is made with sloping sides, which are 80ft. and 60ft. in length. The 80-ft. side is inclined 45 degrees and the other side is 35 degrees to the horizontal. Find the cost of removing the earth at $2 per load, if the trucks have capacity of 4cu. yd.
Answered by Penny Nom.
Three consecutive integers 2008-10-07
From pam:
Find three consecutive integers such that the greatest increased by twice the least is 293.
Answered by Penny Nom & Chris Fisher.
Two consecutive numbers 2008-09-21
From tomas:
what is the two consecutive numbers with a product of 4160?
Answered by Penny Nom.
Cutting a pipe on a 45 degree angle 2008-09-12
From Bakshani:
how do you a mark a pipe 5 inch diameter and cut it to form a 45 degree angel
Answered by Stephen La Rocque.
Three consecutive positive integers 2008-07-20
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.
Product of Two Integers 2008-06-25
From devin:
two consecutive integer have a product of 240. what are they
Answered by Penny Nom.
Two consecutive negative even numbers 2008-06-03
From Chelsea:
The sum of the squares of two consecutive negative even numbers is 100. Find the integers,
Answered by Penny Nom.
Two consecutive odd integers 2008-03-24
From Jarrod:
the sum of two consecutive odd integers is 24. Find the two integers
Answered by Stephen La Rocque.
Two consecutive odd positive integers 2008-03-12
From Sarah:
The sum of the squares of two consecutive odd positive integers is 74. What are th integers?
Answered by Penny Nom.
3 consecutive odd integers 2008-02-28
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.
Classifying a triangle 2008-02-07
From kevin:
scalene triangle 8 ft base right side 9.5 left side 12 ft what is the angles
Answered by Penny Nom.
Three consecutive odd integers 2008-01-24
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.
Find the lengths, and explain in a 'let statement' 2007-12-20
From Cordilla:
the length of the sides of a triangle are 3 consecutive whole numbers. The perimeter of the triangle is 102 meters. Find the lengths, and explain in a' let statement'.
Answered by Stephen La Rocque and Harley Weston.
Three consecutive numbers 2007-12-08
From Aris:
The product of 3 consecutive numbers is 1716. Find their sum.
Answered by Stephen La Rocque.
the sum of two consecutive integers is 51 2007-10-17
From Keira:
the sum of two consecutive integers is 51
Answered by Penny Nom.
Four consecutive integers 2007-09-28
From Joshua:
We were given a question that involved consecutive integers. I can not seem to solve this question and I am the top student in my class.The question states: Find four consecutive integers such that twice the sum of the two greater integers exceeds three times the first by 91. How do you solve this question? Thank you very much for your support.
Answered by Penny Nom, Stephen la Rocque and Claude Tardif.
The sum of two or more consecutive integers 2007-04-26
From nana:
some numbers can be written as the sum of two or more consecutive integers(we consider positive integers only) other number (eg. 4) cannot be express in this way.
let us call a number which can be expressed in this way a SOALTCI( sum of at least two consecutive integers)
a). list the first few SOALTCI and conjecture the general formula.
b). Prove that any number of the given form(in your answer (a)) is a SOALTCI

Answered by Penny Nom.
Determine the probability that the triangle is acute. 2007-04-10
From Greg:
Points A1, A2, . . ., AN are equally spaced around the circumference of a circle and N >=3. Three of these points are selected at random and a triangle is formed using these points as its vertices. If N = 2k for some positive integer k >= 2, determine the probability that the triangle is acute.
Answered by Penny Nom.
Two consecutive odd numbers 2007-03-19
From Alicia:
The sum of two consecutive odd numbers is divisible by 4.

Can you make similar statements about the sum of three consecutive odd numbers and of four consecutive odd numbers? Generalize your findings.

I tried :
n= smallest odd number therefore the next = n, n+2 and the second =n+4 and the third = n+6 Now n+ n+2+n+4+n+6/4
Please help I am not sure of this I am just trying

Answered by Penny Nom.
Choosing numbers with no two consecutive 2007-03-15
From Meghan:
How many combinations are there of 3 numbers chosen from 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 but where no 2 of the 3 numbers are consecutive?

Thank you! -Meghan

Answered by Penny Nom.
Can the triangle be called both an acute triangle and an equilateral triangle? 2007-03-10
From Jane:
If all sides of a triangle are the same length and all angles are 60 degrees, can the triangle be called both an acute triangle and an equilateral triangle?
Answered by Walter Whiteley.
Three consecutive odd integers 2007-01-08
From Emma:
Find three consecutive odd integers such that the sum of the first and second is 27 less than 3 times the third.
Answered by Stephen La Rocque.
Twice the smaller of two consecutive integers is the larger increased by 5. 2007-01-08
From Evan:
Twice the smaller of two consecutive integers is the larger increased by 5. find the integers.
Answered by Stephen La Rocque and Penny Nom.
The sum of 2000 consecutive integers is 1000 2006-10-29
From Matias:
if the sum of 2000 consecutive integers is 1000, then the sum digits of the greatest of these 2000 integers is?
Answered by Penny Nom.
Three consecutive integers 2006-10-29
From Jimmy:
Basically i want to know how you prove that the product of any 3 consecutive integers is a multiple of 6
Answered by Stephen La Rocque.
Three consecutive odd numbers 2006-10-21
From Pige:
The sum of three consecutive odd numbers is 387. Find the numbers.
Answered by Penny Nom.
A board is cut into two pieces... 2006-07-11
From DeAnna:
A 102" board is cut into 2 pieces. One piece is two times the length of the other. Find the lengths of the two pieces.
Answered by Stephen La Rocque.
We are 2 pairs of consecutive 2 digit numbers ... 2006-05-13
From A perent:
We are 2 pairs of consecutive 2 digit numbers that are factors of the number of feet in a mile. Who are we?
Answered by Claude Tardif.
Adding consecutive numbers 2006-04-26
From Lisa:
When I have a total that is the sum of consecutive numbers, how do I figure out what the numbers are?
Answered by Stephen La Rocque.
Divide the product of three consecutive positive integers by their mean 2006-03-12
From Sandy:
When I divided the product of three consecutive positive integers by their mean, I got 99. What is the smallest of the three numbers?
Answered by Stephen La Rocque.
Two consecutive even integers 2006-03-11
From Cheryl:
Find two consecutive even integers that have a sum of 450
Answered by Stephen La Rocque.
Find two consecutive integers whose product is 182 2006-02-09
From Anthony:
Find two consecutive integers whose product is 182
Answered by Steve La Rocque.
The sum of n consecutive integers 2005-11-27
From Craig:

If 875 is expressed as the sum of n consecutive integers (n > 1), then the number
of possible values of n is?

Possible Answers:
A) 15
B) 8
C) 7
D) 16
E) 4


Answered by Penny Nom.
Adding consecutive integers 2005-05-13
From Yas:
i need some help with my work which is to investigating sums of consecutive numbers for example: 15= 4+5+6 and 15=1+2+3+4+5
Answered by Penny Nom.
The least integer of a set of consecutive integers 2005-04-19
From Lucia:
The least integer of a set of consecutive integers is -25. If the sum of these integers is 26, how many integers are in the set?
Answered by Penny Nom.
The length of a cut 2004-09-17
From Florita:
My daughhter, who is a 9th grader is attempting to cut a piece of wood after determining the length of the cut for the hypotenuse. These are the measures: a=4squared, b=6squared.

She determined that c should equal 52. But when she measured the actual piece to be cut, c measured 39.5 inches! Can you offer any insight as to what she is doing wrong? I have suggested that she may be working with an Acute rather than a Right angle . But she insists that it is a Right angle after using a "framing square".

Answered by Claude Tardif.
The product of any n consecutive integers 2004-01-18
From Fazia:
I have to prove that the product of any n consecutive integers is divisible by n!(eg:the product of five consecutive integers is divisible by 5!) It's easy enough to plug in numbers and prove it is true, but i'm finding it difficult to come up with a proper proof.
Answered by Claude Tardif.
Two consecutive negative integers 2004-01-17
From Amanda:
Find two consecutive negative intergers whose product is 182.
Answered by Penny Nom.
Consecutive integers 2003-09-07
From Amy:
I was wondering if there was a proper way to write the solution to a problem requiring consecutive integers? Is it okay to write the solution as 5,4,3,2,1 or must it be written as 1,2,3,4,5?
Answered by Penny Nom.
39 consecutive natural numbers 2003-08-19
From A student:
Prove that among any 39 consecutive natural numbers it is always possible to find one whose sum of digits is divisible by 11.
Answered by Penny Nom.
Cutting some wood 2003-07-25
From Betty:
My husband is building a six sided wood circle and would like to know the angle to cut the pieces.
Answered by Penny Nom.
A pyramid with its top cut off 2003-07-21
From David:
What is the name given to a 3D shape that looks like a pyramid with its top cut off?
Answered by Penny Nom.
positive multiples of 10 that are the sum of four consecutive integers 2003-05-01
From Taurus:
How many positive multiples of 10 that are less than 1000 are the sum of four consecutive integers?
Answered by Penny Nom.
The product of four consecutive integers is 3024. 2003-04-25
From pillar:
The product of four consecutive integers is 3024. What are those numbers.
Answered by Penny Nom.
Divide a circle in 8 equal pieces 2003-04-04
From Naomi:
I have to divide a circle in 8 equal pieces but can only cut 3 times
can you please help me

Answered by Penny Nom.
Three consecutive positive intergers 2003-02-09
From Yew:
Prove that when we multiply any consecutive positive intergers, the result is always divisible by 6.

ex. (7)(8)(9) = 504 = 6 (84)

Answered by Penny Nom.
Cutting a board 2003-01-20
From George:
A person has a sheet of board which he saws into two (2) pieces. The length of the first piece is two thirds the length of the original board, while the length of the second piece is four feet longer than the first piece. How long was the original board? (the length is defined as the longer of the two sides of the board)
Answered by Penny Nom.
Express 5120 as a sum of consecutive numbers 2002-08-25
From Todd:
Express 5120 as a sum of more than 1 consecutive number.
Answered by Leeanne Boehm.
Third side of Acute Triangle 2001-11-09
From Don:
I gave this problem to my children, 9th and 12th grade and they are not(me too!) sure of the answer. I am trying to determine the length of the third side of an acute triangle. I know two of the lengths but I do not know the angles. Is there a proper formula to use to find the length of the third side? Thank you.
Answered by Chris Fisher and Penny Nom.
An acute scalene triangle 2001-09-24
From Kim:
Hi- I'm on a mission--I'm suppose to have a group of children write up a hypotheses about the altitudes and angle biscetors of the follwing 3 types of triangle--equilateral, isosceles and acute scalene triangle.

Is there such a thing as a acute scalene triangle and why or why not.


Answered by Chris Fisher.
Sharing a donut 2001-09-06
From Amanda:
You have invited 11 people over to your house one day, and your friends are hungry. You go into the kitchen and find out you only have 1 donut (with a hole in the middle). In order to feed 12 people (including you), you must cut the donut into 12 pieces with only using a straight knife and cutting 3 times. This is NOT a trick question.
Answered by Claude Tardif.
4160 2001-03-07
From Jessica:
The product of two consecutive page numbers in this book is 4160. What are the page numbers?
Answered by Penny Nom.
A pole next to a building 2001-02-20
From Robert L. Haun:
A pole 100 feet tall is erected next to a building 10' X 10' X 10' . Object is to cut off the pole so the upper end remains touching the part cut off, while the cut-off portion touches the cutoff point, the edge of the building and the ground. Note assume the pole is touching the building and is "very thin" What is/are the cutoff points?
Answered by Penny Nom.
Crown molding mitre cuts 2000-11-06
From Jim Tomfohrde:
My question has to do with making mitre cuts when installing crown molding. Crown molding is the trim that is put up at the top of walls with one edge on the wall and the other edge on the ceiling. To make a mitre cut on your mitre saw for a 90-degree corner you can lay the molding flat on the saw base, set the bevel of the blade to 34 degrees and the mitre to 31.5 degrees (these may be slightly appoximate). Of course depending on which piece of molding you're cutting you will cut one end or the other, or use the left or right end. These angles allow the cuts to line up and form a seamless corner when they're put in place on the wall/ceiling at 90 degrees. My question is this - is there some mathematical formula from which the 34 degrees and 31.5 degrees are derived. I want to know this because in many cases the corner is not 90 degrees but can be more or less, and in these instances I would like to know if I can calculate the bevel and mitre to use based on the angle of the corner.
Answered by Harley Weston.
Cutting the lawn 2000-10-26
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.
Three consecutive odd integers 2000-08-18
From Wallace:
A six-digit 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.
Cutting a carpet 1999-12-15
From Heather:
A rectanglular piece of carpeting is 90 inches long and 90 inches wide. How can the carpet be cut into two pieces of equal sides and shape to cover an area of 100inches? There can only be one cut and no scraps. Please show me how.
Answered by Penny Nom.
Ratios and proportions 1999-11-19
From Rebecca:
I'm not that good of a student and I was woundering if there is a shortcut to ratios and proportion. My 6th grade teach tought all we needed to know. I was just wounder if there was an easier way.
Answered by Claude Tardif and Harley Weston.
Cutting a board into 8 equal pieces 1999-10-21
From Brittany:
Jamie wanted a board cut into 8 equal pieces. The Lucas Lumber Co. charges 60 cents for cutting a board into 4 equal pieces. How much will it charge for cutting Jamie's board?
Answered by Claude Tardif.
Deux nombres consécutifs 2010-01-18
From Janot:
Bonjour comment peut on faire pour démontrer que si deux nombres sont consécutifs, leur produit et leur somme sont premiers entre eux Merci de me mettre sur la voie , j'ai échoué avec Bezout.
Answered by Claude Tardif.
La somme de 51 nombres entiers consécutifs est 1785 2003-04-01
From Katrine et Armand:
La somme de 51 nombres entiers consécutifs est 1785, quels sont ces nombres? (indication : on rappelle que pour tout entier P, on a 1 + 2 + ....+ P = P (P + 1) / 2).
Answered by Claude Tardif et Penny Nom.
 
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