







The wholesale price given the retail price and the markup 
20180207 

From Matthew: Retail $99
Markup is 80%
What is the equation to find the original (wholesale) price (55)?
thanks Answered by Penny Nom. 





Average price 
20170915 

From Annette: If I sold a widget at $15.50 17.5% of the time and $16.50 88.5% of the time what is the algebraic expression for that. How do I arrive at an average price Answered by Penny Nom. 





What is the regular price? 
20170511 

From Saira: If the sale price is 55.50$ and the discount is 12% what is the regular price Answered by Penny Nom. 





Selling price and markup 
20170424 

From Julie: What would the cost of an item be, if the sell price was $50 and the markup 48% Answered by Penny Nom. 





How do I establish the original List Price? 
20170115 

From Bob: (1) I have a net price item at $4,664.66 but do not have the discount percentage. I have been told I received 40%? How do I establish the original List Price and to confirm what discount I received? Answered by Penny Nom. 





Selina saved $6 on a 20% off sale 
20161014 

From Myra: I don't know how to help my child answer this question  Selina bought a shirt on sale that was 20% less than the original price. The original price was $6 more than the sale price. What was the original price? Answered by Penny Nom. 





A 15% discount 
20160809 

From eunice: brian brought a printer sale at the store. the discount was 15%, and brian saved 550. what was the printer original price? Answered by Penny Nom. 





A 70% off sale 
20160511 

From virginia: If the sale price is $129.99 @ 70% off  what was the original price? Answered by Penny Nom. 





The original price before a discount and taxes 
20151209 

From Michelle: Good day,
I would like to know if there is a particular equation to validate the following information:
I had to find the original cost of an item sold for 759.36$ before a 25% discount and 13% taxes.
I know we must use separate question to obtain the answer but I am unsure how to write the equation to validate my answer. Answered by Penny Nom. 





Two price reductions and a coupon 
20150916 

From Suszanne: Mary purchased an item for 45% off the original price, plus an additional 20% off the sale price.She also had a $5 off coupon, which the salesclerk applied after these two discounts. Mary's final purchase price for the item was $50. She paid no sales tax, what was the original price of the item? Answered by Penny Nom. 





Order of operations 
20150912 

From Tanisha: I would just like to double check if something like 5x squared times 4x cubed equals 20x to the power of 5??
It's just that we were told you can only answer an equation like this if the base is the same...so does that mean the x part or the whole thing like 5x?
I'm sorry if that didn't make sense!
Thank you for your help!! Answered by Penny Nom. 





A cone of maximum volume 
20150316 

From Mary: I have to use a 8 1/2 inch by 11 inch piece of paper to make a cone that will hold the maximum amount of ice cream possible by only filling it to the top of the cone. I am then supposed to write a function for the volume of my cone and use my graphing calculator to determine the radius and height of the circle. I am so confused, and other than being able to cut the paper into the circle, I do not know where to start. Thank you for your help! Mary Answered by Robert Dawson. 





What is our cost? 
20150127 

From Johanna: I have a pieces of 3/4" sch40 (round tube) 240" long at $70. What is our cost. We also add 35% to our cost for selling price. How do I figure this out? Answered by Penny Nom. 





Selling items at a reduced price 
20150109 

From Kent: I have an item I sell for $19.95 and make a profit of $10.97 for each sale.
If I reduce the price to $14.97, my profit is $5.99 each sale.
Is there a formula to determine how many more I would need to sell
at $5.99 per sale to make the same net cash (profit) as selling at $10.97 per sale? Answered by Penny Nom. 





A price increase and a consumption decrease 
20140816 

From sujan: If the price of petrol increases by 25% and Rajesh intends to spend only 15% more on petrol then by how much % should he reduce the quantity of petrol he buys? Answered by Penny Nom. 





Speed, distance, time 
20140813 

From Aarti: a theif running at 8 km/hr is chased by a policeman whose speed is 10km/hr.if the thief is 100 m ahead the policeman then what will b time required for the policeman to catch the thief? Answered by Tyler Wood. 





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. 





A conditional probability problem 
20140413 

From Chiluya: Two fair dice are rolled. what is the probability that the number on the first die was at least as large as 4 given that the sum of the two dice was 8? Answered by Penny Nom. 





Graphing piecewise functions 
20140329 

From Rayven: Hi! I'm in eighth grade, taking ninth grade algebra 1. I'm confused as to how to
graph piecewise functions. I know that you have already answered a question similar to this
(I did my research first) but it didn't completely help me on my homework. I have to graph
piecewise functions for the specified domains, and create a table for the absolute values.
I know that two bars around a number means absolute value (two bars around 2 makes it +2)
, but how do I graph and chart the absolute value for the following:
f(x)= x+3  for 5≤x≤3
And then graph and chart: (on a separate graph):
f(x)= {x if x≤0
{x+1 if x <0
thank you!
~Rayven Answered by Penny Nom. 





Determine the selling price 
20140308 

From augustine: knowing an auctioneer charges a 7% fee and I know I want $74,400 what is the formula to determine selling price. Answered by Penny Nom. 





Finding the retail price 
20140222 

From Judy: An item is currently on sale at 37% off the retail price. The item now sells for $350.
My Question:
What is the retail price and what is the formula or steps to figuring that out? Answered by Penny Nom. 





A sale price for a TV 
20131128 

From tom: a TV can be purchased for $278 normally is $328. what is the percent of the present cost of this TV will you be saving? Answered by Penny Nom. 





Matrices 
20131110 

From Ricky: Why must we have brackets around matrices. Why don't we just neatly write an array of entries crosswise and up and down to indicate a particular matrix? Answered by Chris Fisher. 





Price, revenue and profit 
20130922 

From lorraine: What price maximizes revenue? What price maximizes profit?
The only data I'm given is total output, total revenue, and total cost.
I'm not sure how to set up a formula Answered by Penny Nom. 





Dice 
20130514 

From Julia: What is the probability of rolling(as many times as necessary) a die and getting a total number(sum) when all the rolls are added together of 11? Answered by Lorraine Dame. 





What is the original price? 
20130425 

From Dylan: shirts on sale for 25% off, the sale price is 12.75. What is the original price? Answered by Penny Nom. 





Row echelon form 
20130315 

From Shawn: Please help me put matrix in row echelon form:
1 9 8 0
5 8 1 35
1 4 1 17 Answered by Penny Nom. 





Markup and discount to get a sale price 
20130302 

From Warren:
If you are an ardent shopper you will be aware of the discount (% decrease) marketing strategy to produce the sale price. I began to wonder just how much markup (% increase) was added initially to an item in order to deliver the discounted sale price.
It was simple to construct a formula to convert one to the other.
For example a 30% (mark down) decrease in price required a 42.86% (mark up) to increase the price initially to Tag price. However when I started apply the formulae to a number of circumstances I noticed some very interesting circumstances associated with this relationship
For example a 99.999999% decrease is numerically equal to a 9,999,999,925% increase (huge ratio difference) while conversely a 0.1% decrease is numerically equal to a 0.10010010% increase (Infinitesimally small ratio difference) so the patterns appears logarithmic not linear.
However what really caught my attention was this pattern
See http://www.ozsmart.com/doc/percentage.htm
My questions is why does the decline in the ratio of increases in required mark up (%) price peak at 50 and 51% precisely and then expand again as the percentage move higher
Any explanation would be appreciated Answered by Harley Weston. 





Your profit should be 20% of your cost 
20130221 

From anis: if the customer says your profit should be 20% of your cost..
1) my selling value should be cost +20% of cost = SP
or
2)cost / 0.80 = SP which is correct...if the second answer is right how should i justify my customer 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. 





The area of a triangle given its vertices 
20121127 

From elizabeth: how to calculate the area of a triangle using points ABC a (2,5) b ( 4,3) c ( 6, 1) Answered by Penny Nom. 





The difference of the numbers on two dice 
20120819 

From dilys: Two fair dice are thrown. Find the probability that the difference of the two numbers is divisible by 4? Answered by Chris Fisher and Lorraine Dame. 





The maximum distance from the vertex of a triangle 
20120502 

From David: There are three towns A,B,and C, equidistant apart.
A car is 3 miles from town A, and 4 miles from town B.
(ie, somehwere outside of the triangle which the three towns form)
What is the maximum distance that the car can be from town A?
This was asked as quiz question in my local pub last Sunday.
The answer is 7. How do I prove it?
Best regards. David in Denton. Answered by Robert Dawson and Chris Fisher. 





What is the better price? 
20120330 

From john: What is the better price?
If a bag of mulch sells for $6.75 and contains 2.7 cubit feet versus a bag selling for $5.99 and contains 2 cubit feet.
Which is the better value? Answered by Penny Nom. 





The price per square inch of a pizza 
20120317 

From jordan: pizzaz pizza sells a small pizza for $10.99.it has a diameter 10 inches.what is th price per square inch ? Answered by Penny Nom. 





Rolling three dice 
20120126 

From Aishwarya: A red, a blue and a green die are all thrown at the same time. Display all the possible outcomes in a suitable way. Find the probability of obtaining:
1. A total of 18 on the three dice
2. a total of 4 on the three dice
3. a total of 10 on the three dice
4. a total of 15 on the three dice
5. a total of 7 on the three dice
6. the same number on each die.. Answered by Robert Dawson. 





A cube of ice is melting 
20111205 

From Emily: a cube of ice (i.e.) each side is of the same length) is melting at a rate such that the length of each side is decreasing at a rate of 5cm per hour. how fast is the volume of the cube decreasing (in cubic cm per hour) at the instant the length of each side is 25cm? Answered by Penny Nom. 





What was the cost price of the article? 
20111110 

From tashana: By selling an article for $320,the profit was 20% of the cost price.what was the cost price of the article. Answered by Penny Nom. 





6 faces and 8 corners 
20110304 

From noemi: jeff made a figure with 6 faces the figure has 8 corners all of the faces are the same size and shape what figure did jeff make Answered by Penny Nom. 





Vertices and sides of a polygon 
20110304 

From RINA: My questions is : would a vertices and sides of a polygon be the same number. For example, a octagon it has 8 points and 8 sides. Am i correct? Answered by Robert Dawson. 





The height of an iceberg 
20101216 

From Sharon: if an iceberg can be seen 10% or 70 meters above the water, what is the measurement in meters of the iceberg below the surface of the water? Answered by Robert Dawson and Penny Nom. 





Geocaching 
20101015 

From Clint: I am stuck on a puzzle for Geocaching which is a GPS game.
I know it is a number matrix but don't know how to start.
[1 7 16 3 9; 1 3 18 20 33] x [1 8 9 3 5; 0 1 0 4 2; 0 0 1 2 1; 0 0 0 1 1; 0 0 0 0 1] = ? Answered by Stephen La Rocque. 





Selling price, cost and profit 
20100622 

From Alex: The profit on a certain television set is 16.5% of the cost price. If the profit is $330,
Find:
a) the cost price
b)the selling price of the television Answered by Penny Nom. 





The vertices of an equilateral triangle 
20100219 

From Emma: If two of the vertices of an equilateral triangle are (2,1) and (6,5), what
are the two possible coordinates of the third side of the triangle? Answer
in radical form. Answered by Tyler Wood. 





The price before tax 
20100215 

From dawn: the sale tax on a cape was 6%,and total price with tax was $92.75,what was the price of the cape? Answered by Penny Nom. 





A triangular pyramid 
20100105 

From ally: how many vertices, edges, faces in a triangular pyramid? Answered by Robert Dawson. 





Find the original price 
20091106 

From Cyndy: Find the original price of a pair of shoes if the sale price is $98.00 after a 30% discount. Answered by Penny Nom. 





Commodity price increase 
20091104 

From bharat: if price of a commodity increases by x% the to keep the expenditure same
the decrease in consumption should be (x/(x+100))*100, why? Answered by Penny Nom. 





A single die is rolled twice 
20091103 

From Michelle: A single die is rolled twice. Find the probability of getting two numbers whose sum exceeds 5.
I can't seem to come up with any of these answers, Help. A. 0.72 B. 0.89 C. 0.68 D. 0.58 Answered by Penny Nom. 





Toss a coin and roll a die 
20090921 

From Celeste: Can you please tell me how to set up this problem to find the answer. I know they are independent from there I don't know.
a coin and a regular sixsided die are tossed together once. What is the probability that the coin shows a head or the die has a 5 on the upward face? Answered by Penny Nom. 





A trillion grains of rice 
20090914 

From akaila: can 1trillion rice grains fit in a classroom with the area of 144.4m3 Answered by Penny Nom. 





Price increases and decreases 
20090902 

From craig: I work for an industry that bases it price increases and decreases on commodity pricing  Customer get confused on how/why we calculated new prices due to movement in the market 
Price go up x% for every $10 of movement in the market 
For this example
Movement went down by $30 and it is 2% for every $10  so price decrease was 6%.
Customer's price is currently $100.
We say  $100/1.06= new price of $94.3
Customer says  $100*.94= new price of $94.
They don't understand that if board went back up $30 which would be 6% increase, they wouldn't be back at $100 if they multiplied on the price decrease.
$94*1.06=$99.64 vs. $94.3*1.06=$100 (Back to the original price)
What is the best way to explain to customer besides using this example?
Any help or info is appreciated.
Craig Answered by Victoria West. 





Percentage price change 
20090827 

From alicia: what is the percentage price change between R66R10 if the answer between the two is R56 Answered by Penny Nom. 





The taxable part of an invoice 
20090825 

From Carol: Question from CAROL:
THE INVOICE TOTAL IS 2731.90 BUT IT DOES NOT SHOW WHAT THE NET AMOUNT IS
THAT THE STATED GST OF 121.90 IS. HOW DO I CALCULATE THE NET AMOUNT THAT
THIS GST AMOUNT REFERS TO? Answered by Harley Weston. 





Torricelli's trumpet 
20090729 

From Gary: I was reading about torricelli's trumpet which is described by the equation1/x which is then rotated around the x axis which results in a figure which looks like a trumpet. Now in order to find the volume the integral 1/x^2 dx is used which diverges when integrated so the volume is finite.However if you integrate 1/x dx which is the formula on the plane the answer diverges. Now if you took an infinite area then rotated it around the x axis shouldn't you get an infinite volume? Notice the area I am talking about is under the line 1/x not the surface area of the trumpet which is what the painters paradox is about What am I missing? Thanks Answered by Robert Dawson. 





The retail price for an ice cream scoop 
20090705 

From Patricia: Hi  I am trying to figure out the fairest retail price for an ice cream scoop. We have an ice cream parlor
and the cost of the ice cream we buy by the bulk container has recently been increased so now we must charge
more for our scoops. We pay a wholesale price of $25.40 for 242 ounces of ice cream. The cost per ounce is
$0.105. What is the formula for figuring out how much to charge retail per scoop? This is probably so simple
but confusing to me. Please help. Thank you! Answered by Harley Weston. 





Unit Price 
20090608 

From MATTHEW: Question from Matt:
I quoted my customer $112.50 per 1,000 sheets per linear yards. My client said I was to high. I need to be at 18 cents per square inch. If I matched his 18 cents per square ines what would my linear yards per 1,000 sheets price be? It comes on a 12.5 inch roll. Answered by Janice Cotcher. 





Two dice and the difference of squares 
20090421 

From dave: I dont understand how to do this: Two fair dice are rolled. What is the probability that the difference of the squares of the numbers is divisible by three? the answer is 5/9 Answered by Harley Weston. 





Choices at a restaurant 
20090413 

From Rob: There is a restaurant you get:
Rice/Noodles (1) 
Main Ingredient (any) 
Sauce (1) 
1 
1 
1 
2 
2 
2 
3 
3 
3 
4 
4 
4 
5 
5 
5 
6 
6 
6 
7 
7 


8 


9 


10 


11 


12 

So the question is how many different combinations are there. You can only have 1 rice/noodles in a selection and only 1 sauce in a selection but you can have between 1 and all twelve mains in a selection. there are 7 rice/noodles , 12 mains and 6 sauces. How many possibilies. I did it mentally in the restuarant, no pen, paper or calculater and i got 3276..i think thats wrong. please help
Rob Answered by Robert Dawson, Stephen La Rocque and Claude Tardif. 





The axiom of choice and constructibe sets 
20090410 

From sydney: The axiom of choice asserts the existence of certain sets, but does not construct the set. What does "construct" mean here? For example, does it require showing the existence and uniqueness of some function yielding the set? In general, what does it mean to require the existence of a mathematical object be tied to a construction of it? Answered by Claude Tardif. 





A large, hollow, ice cream cone 
20090403 

From Darah: A manufacturer is making a large, hollow, ice cream cone to serve as an ad for a local BaskinRobbins. The ice cream cone is made up of a cone with height 8 feet, topped by a hemisphere with radius 6 feet. How much ice cream could the hollow object hold? If a gallon is 0.13368 cubic feet, how many gallons does it hold? If 3 gallons of BaskinRobbins heavy cream chocolate blend weighs 24 pounds, how much would the ice cream cone weigh, excluding the weight of the construction material? Answered by Stephen La Rocque. 





Grain of rice on a chess board 
20090330 

From andy: Is there an easy way for my students to find out 8 to the power of 21 to solve the grains of rice doubling investigation on a chessboard? Any suggestions welcome. Thanks very much Answered by Robert Dawson and Claude Tardif. 





Find the retail price 
20090318 

From Allie: If you have food that costs $0.75 per portion and your food cost is 16.5% how would you find the retail price? Answered by Penny Nom. 





License plates and poker hands 
20090314 

From CC: You have a license plate it can have 6 numbers/letters you can use the numerals 09 and the letters AZ how many combos are possible and how did you figure it out?
Question 2,
Your dealt an Omaha hand You have KKKQQ, how many different hands can consist of the same cards. Answered by Harley Weston. 





15 flavors of ice cream 
20090311 

From Pedro: I was given this word question an was somewhat confused can u help me understand.
An ice cream vendor sells 15 flavors of ice cream and u want to sample at least
4 different types. how many different combinations of ice cream would u be able
to sample? Answered by Penny Nom. 





A shape with 10 sides 
20090303 

From Sandra: One of my son's math questions is as follows:
Suppose I have a shape with 10 sides. I choose a vertex then draw lines to the other vertices that dont share sides with the first vertex. How many vertices will that be and why? Answered by Penny Nom. 





A triangular pyramid 
20090226 

From Craig: Can you help with this question:
Write the names of the faces and the number of each kind of face on a triangular
pyramid? Answered by Penny Nom. 





Vertices, edges and faces 
20090219 

From Deb: I have been reading the responses you have to whether or not a cone and cylinder have edges, and whether a cone has a vertex. I have also found differing answers in different books and websites. Your idea that it depends why we want to call it a vertex or edge is interesting but does not help the students next year when they have a different teacher who tells them that whatever decision I make is wrong! It also doesn't help them when they do the provincial testing. Does anyone know if EQAO considers them vertices or edges? I want to know because textbooks and provincial tests often ask the students to count the number of faces, edges, and vertices or to describe a solid by using these, or to identify a solid that they have described. We need to have consistency in what we are teaching! Answered by Chris Fisher. 





The column space of a matrix 
20090212 

From John: Question from John, a student:
A=
1 1 0 0
1 1 0 0
0 0 1 0
0 0 1 1
B=
1 5 6
1 5 6
0 7 2
0 0 9
Is the space spanned by the columns of A the same as the space spanned by the columns of B? Answered by Harley Weston. 





Faces, edges and vertices 
20090204 

From sheila: what is the relationship between the number of faces and the number of edges of a triangular pyramid ? Answered by Penny Nom. 





Calculating markup 
20090203 

From Tonya: I'm trying to figure out the formula for the following, I have a product that I want to receive a certain profit, but with this product I also have to pay a percentage of commission to someone. I need to know how to calculate my new selling price taking into account the markup percentage, but I don't want my cut to be lowered. I have calculated the markup percentage to get my new selling price with the commission, but it lowers my cut once I pay the commission and I don't want it to do that. Thanks Answered by Penny Nom. 





A die is loaded so that... 
20090130 

From Larry: Hi. I'm having trouble solving this problem. Would you be kind enough to point me in the right direction?
A die is loaded so that the probability of a particular face rolling up is proportional to the number of dots
on the face. In other words, getting a six is three times as probable as getting a two. what is the probability
of getting an even number in one toss? Answered by Victoria West. 





PST and GST 
20090120 

From janet: Hello
I need to figure what one would pay pst 8% gst 5% on a total of $1700.00
I have a small business some pay with cash I need to calculate the taxes in reverse Can you help with formula that the government might like
Thank you
Janet Answered by Harley Weston. 





License plates 
20081117 

From Clayton: Okay, so in this situation a license plate must have four letters (AZ) and four numbers (09), ex. ABCD1234, where repeating a letter or number is allowed ex. AAAA1234, or ABCD1111, or AAAA1111. The order of letters first numbers second, or number first, letters second is allowable, and each state has its own plates, so ABCD1234 from New York, and ABCD1234 from Minnesota are considered different combinations, how many different license plates could there be? Answered by Penny Nom. 





Confusion in a multiple choice question 
20081114 

From BJ: My son got this math problem which he could mostly solve. Here it is:
The highest location in a certain country is 4525 m above sea level. The lowest point in the same country is 192 m below sea level.
a) Find the difference of the two elevations. His answer: a(b)= a+b or 4525(192)= 4525+192=4717 m. No problem.
b) A city is 2221 m above sea level. Is this elevation closer to the highest point or the lowest point?
His answer: highest point because: 45252221= 2304 m (closest to the highest point) and 2221(192)=2221+192= 2413 m. (farthest to the lowest point). OK so far.
But then he was given 4 choices for this question with no other information:
a) 4717 m; lowest b) 4333 m; lowest c) 4333 m; highest d) 4717 m; highest
What does it mean? What's the connection with the rest of the problem? Answered by Harley Weston. 





The volume of a slice from a wedge 
20081016 

From Jeff: If I have a wedge shaped object (ie, a triangle of nonspecific type
extruded along a length) and it is sliced from the twocorner base at
one end to the onepoint tip at the other, what is the volume of the
upper (smaller) part as a percentage of the whole? I hope I have
explained it clearly enough. Thanks. Answered by Harley Weston. 





The vertices of a triangle 
20080927 

From T.: how do you find the coordinates of the vertices of the triangle with the sides determined by the graphs of the following equations:4x+3y+1=0,4x3y17=0,4x9y+13=0? Answered by Harley Weston. 





A multiple choice exam 
20080913 

From Phalange: A multiple choice exam consists of 12 questions, each having 5 possible answers. To pass, you must answer at least 9 out of 12 questions correctly. What is the probability of passing if:
a. You go into the exam without knowing a thing, and have to resort to pure guessing?
b. You have studied enough so that on each question, 3 choices can be eliminated. But then you have to make a pure guess between the remaining 2 choices.
c. You have studied enough so that you know for sure the correct answer on 2 questions. For the remaining 10 questions you have to resort to pure guessing. Answered by Harley Weston. 





A price reduction and a discount 
20080911 

From Rita: A store advertises that during its Labor Day sale $15 will be deducted from every purchase over $100. In addition, after the deduction is taken, the store offers an earlybird discount of 20% to any person who makes a purchase before 10 a.m. If Hakeem makes a purchase of x dollars,
x > 100, at 8 a.m., what, in terms of x, is the cost of Hakeem's purchase?
(1) 0.20x  15 (3) 0.85x  20
(2) 0.20x 3 (4) 0.80x  12 Answered by Penny Nom. 





The selling price 
20080904 

From Robert: Client wants to sell his property providing he is left with 100000.00$ net.
How do I calculate selling price if commission is 6% and taxes on the commission 6% Fed and 7.5%prov.
I'm taking the real estate class and this one really got me. Answered by Penny Nom. 





A linear system 
20080823 

From dipesh: consider the system of equations
x6y+2z=5
2x9yz=14
4x+12y3z=19 by reducing the augm matrix to row echelon form, find
the solution to the equation.
leaving the first two equations the third is changed to 3x+6y+14z=31
show the equations have infinitely many solutions and give a general
formula for them Answered by Penny Nom. 





Joining vertices in a polygon 
20080818 

From Megan: I'm trying to develop a relationship between the number of points of a regular polygon and the
(a) number of lines you could draw between those points,
(b) number of triangles you could draw,
(c) number of quadrilaterals,
etc. Answered by Penny Nom. 





What is the GST component? 
20080611 

From Jilly: I need to find a quick and easy formula for finding the gst (10%) of the total amount in $ terms, eg: the total is $500 what is the gst component? Answered by Penny Nom. 





Calculating a price based on markup 
20080603 

From Sheldon: I know the most common form for retail businesses of calculating a price based on markup is:
Cost/(1  Markup), but how is this supposed to work for a business that desires a markup of over 100%. Answered by Harley Weston. 





Selling price 
20080510 

From Roxane: I'm trying to figure out the formula for the following, I have a product that
I want to receive a certain profit margin, but with this product I also have
to pay a percentage of commission to someone. I need to know how to
calculate my new selling price taking into account the markup percentage, but
I don't want my gross margin to be lowered. I have calculated the markup
percentage to get my new selling price with the commission, but it lowers
my profit margin once I pay the commission and I don't want it to do that. Answered by Penny Nom. 





Determinants 
20080502 

From Henry: I have a question about solving 3x3 matrices.
The traditional way, or at least the way I've been taught, is that if one has a 3x3 matrix such as:
[ a b c ]
[ d e f ]
[ g h i ]
one solves it according to this formula:
[ei  hf)  (bi  hc) + (bf  ec) = determinant.
According to a book I'm now studying to prepare for the California CSET exam, there is another, easier, way to solve it:
[ a b c ] [ a b ]
[ d e f ] [ d e ]
[ g h i ] [ g h ]
In other words, one repeats the first two rows of the matrix and adds them to the right.
At this point, the determinant is calculated thus:
(aei) +(bfg) + (cdh)  (gec)  (hfa)  (idb).
Is this, in fact, correct? Answered by Harley Weston. 





The maximum area of a pizza slice 
20080412 

From charles: A slice of pizza in the form of a sector of a circle has a perimeter of 24 inches. what value for the radius of the pizza makes the slice largest[when o is the central angle in radians, the area of the sector is given by A= r^20/2and the length on the circle is given by s=r0 Answered by Harley Weston. 





Matrix multiplication 
20080408 

From manashi: i. why matrix division is not possible?
ii.when we add or subtract two matrix , getting the result by addind or subtracting correspondind elements....but in case of multiplication it is not but why? Answered by Harley Weston. 





A shape 
20080403 

From Joshua: what shape has 4 faces, 4 corners and 9 edges. Answered by Penny Nom. 





The number of faces and vertices in a pyramid 
20080402 

From Laurie: Can you find a connection between the number of faces and vertices in a pyramid and the number of sides of it's base??? Answered by Penny Nom. 





Some solid figures 
20080228 

From tiffany: What solid figure could have? It has 4 more edges than vertices, Answered by Penny Nom. 





Rolling a 5 before an 11 
20080227 

From Jeremy: If rolling two sixsided dice, what is the probability that a sum of 5 will be rolled before a sum of 11? Answered by Stephen La Rocque and Harley Weston. 





A line drawn between 2 vertices 
20080226 

From Arshad: what is a line drawn between 2 vertices which are not next to each other called. Answered by Penny Nom. 





Actural cost, selling price and commission 
20080221 

From LiSa: I have a question about a few things if anyone can answer...
ex.
actual cost (AC) = $1000
selling price (SP) = $
amount earned for company (C) = 15% of... selling price?
commission 1 (C1) = 2.5%
commission 2 (C2) = 2.5%
How would you calculate how much the company's commission amount would be as well as the amounts for the other 2 that get 2.5%? And what would the selling price be? (the 15% $ + 2.5% $ + 2.5% $ ?)
Is the 2.5% taken from the original amount? I am soooo confused!
If anyone could help, that would be great! Answered by Harley Weston. 





How many different hamburgers is it possible to order? 
20080217 

From Elizabeth: At a hamburger stand you can order a hamburger with any of the following, in any combination: ketchup, mustard, pickles, onions, tomatoes, mayonnaise and/or lettuce. How many different hamburgers is it possible to order? Answered by Penny Nom. 





What solid figure has 1 flat surface and 0 vertices? 
20080130 

From Cheronda: What solid figure has 1 flat surface and 0 vertices? Answered by Stephen La Rocque and Harley Weston. 





Sides and vertices 
20071117 

From derek: What is the correct name for a 2D geometric shape that would look like one slice from a round pizza and how may sides and vertices would it have? I believe you would say it has one vertex and two sides with the curved boundary not resulting in vertices or a side. Your help is much appreciated. Answered by Chris Fisher and Walter Whitelty. 





The best price for topsoil 
20071115 

From Dawn: What is a better deal for topsoil, $150.00 for 10 cubic yards, $170.00 for 22 tons, or $200.00 for 11.5 yards? Answered by Penny Nom. 





A line between 2 vertices 
20071028 

From robert: what do we call a line between 2 vertices which are not next to each other Answered by Walter Whiteley. 





Rolling a die repeatedly (you can't just add percentages) 
20071004 

From Howard: If my son has a 16.66% chance of rolling a particular number on a dice,
and he rolls for it 6 times, he knows (from experience) that his
odds of getting at least 1 right are not 100% (16.66% +16.66%+16.66% etc).
He asked me if there was an equation that would give him the correct
percentage chance of success when trying X times for a Y% chance
of something. Answered by Victoria West. 





Cubic meters, square feet and office space 
20070925 

From Kathryn: Can someone please help and let me know how do you convert 11 cubic meters into square footage? Answered by Steve La Rocque and Harley Weston. 





The diagonal of a square 
20070923 

From Nasreen: A(7,2) and C(1,4) are two vertices of a square ABCD
find in the form ax+by=c the equation of the diagonal BD Answered by Stephen La Rocque. 





Vertices 
20070918 

From Richard: Please help. Do not understand vertices, as in how many in a cone, hemisphere, etc. Answered by Harley Weston. 





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. 





Twenty dining tables 
20070813 

From priya: Utkarsh bought 20 dining tables for Rs 120000 and sold these at a profit equal to the S.P of 4 dining tables.Find the S.P of one dining table.(give the answer in statements) Answered by Stephen La Rocque. 





Guessing multiple choice answers 
20070724 

From carla: You are taking a multiple choice quiz that consist in 3 questions, each question has
3 possible answers only one is correct. To complete the quiz you randomly guess the answer
to each question . Find the probability of guessing exactly 2 answer correctly. b) at least to answer correctly . c)less than two answer correctly Answered by Stephen La Rocque. 





A triangular pyramid 
20070722 

From shani: my homework question is confusing (yr 7 beginner)
"How many vertices does a triangular pyramid have."
(Mum thinks all triangles are triangular& vertices are sides)
I want to be sure. Answered by Penny Nom. 





Discount percentage 
20070711 

From Greg: List Price: $50.00
Discount: 33 1/3%
What would the net price be? Answered by Stephen La Rocque. 





The probability of rolling double sixes twice in a row 
20070710 

From Matt: what is the probability of rolling double sixes twice in a row? Answered by Stephen La Rocque. 





How fast was he going? 
20070603 

From Mary: if a motorcycle left a 63 foot skid mark before hitting a car how fast was he going ? Answered by Penny Nom. 





The difference between two dice 
20070602 

From smiley: Two standards dice are rolled. Determine the probability
that the difference between the two numbers on the dice is 2 Answered by Penny Nom. 





Hexagonal pyramids 
20070517 

From Tracey: How many faces, edges, and vertices does a hexagonal pyramid have? Answered by Stephen La Rocque. 





What's a vertex? What's an edge? 
20070516 

From Sophie: I don't understand what is a vertex and what is an edge. Please put a picture up and explain. I am a fifth grader. Answered by Brennan Yaremko and Steve La Rocque. 





The vertices of a triangle 
20070502 

From natakie: Find the coordinate of the vertices of a triangle whose sides lie on the following three lines.
2x+5y16=0, 4x3y6=0 and 3x+y+2=0 Answered by Penny Nom. 





Vertices, edges and faces 
20070419 

From Kimberly: I am trying to help my son find the vertices, edge, and face of a 16 sided figure.
I am not sure of the process to use to find these, could you please tell me
how to do this? Answered by Penny Nom. 





Which solid figure has 4 more edges than vertices? 
20070322 

From dawn: which solid figure has 4 more edges than vertices? Answered by Penny Nom. 





Rolling two dice 
20070306 

From Mary: I have a test and I need to know how to figure out how to find the probability of rolling 2 dice and coming up with a 7 for both rolls. Could you please explain how to find the probability? Thank you. Mary Answered by Penny Nom. 





What constitutes a face for a geometric solid? 
20070214 

From Erica: What constitutes a face for a geometric solid? We have been getting conflicting answers from different textbooks. Some teachers are saying that cylinders and cones do not have faces. I'm thinking that cylinders have 2 and cones have 1. Please enlighten me. Thanks! Answered by Walter Whiteley. 





A margin of 19% 
20070201 

From Ed: I PAY $10.95 FOR THIS PRODUCT, HOW SHOULD I PRICE IT IN ORDER TO HAVE A MARGIN OF 19% COST. Answered by Penny Nom. 





At the ice cream parlor 
20070110 

From Bill: at the ice cream parlor, customers can chose among five different ice cream flavors and can choose either a sugar cone or a waffle cone. considering both ice cream flavor and cone type, how many distinct triplescoop with three different ice cream flavors are available? Answered by Penny Nom. 





A cylinder has how many flat surfaces, vertices, and edges? 
20070109 

From Stacy: A cylinder has how many flat surfaces, vertices, and edges? Answered by Diane Hanson and Penny Nom. 





How many licence plates are possible? 
20061124 

From Naomi: The state of New York has licence plates with five numbers followed by either a letter A or a letter B (eg. 36457A ,59972B ). How many licence plates are possible? Answered by Penny Nom. 





Lattice multiplication 
20061016 

From Patti: I am a parent of a 5 th grader, and am a bit loss in the "new" math. I know how to multiply using the "old fashion" method. But, could you please explain lattice multiplication. Answered by Diane Hanson. 





A board is cut into two pieces... 
20060711 

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. 





What is the probability that the policeman will shadow the correct person? 
20060614 

From Kolby: Through an informer from the underworld, the police know the meeting place of a gang. The identity of the different gang members, however, is unknown. it is the duty of a policeman to shadow the leader of the gang. The policeman knows that the leader is the tallest of the five persons, all of whom have different heights. after the meeting, the gangsters, as a safety measure, leave the building separately at intervals of 5 minutes. As the policeman cannot see who is the tallest, he decides to let the first two gangsters go and shadow the one after that who is taller than all those who left before.Through an informer from the underworld, the police know the meeting place of a gang. The identity of the different gang members, however, is unknown. it is the duty of a policeman to shadow the leader of the gang. The policeman knows that the leader is the tallest of the five persons, all of whom have different heights. after the meeting, the gangsters, as a safety measure, leave the building separately at intervals of 5 minutes. As the policeman cannot see who is the tallest, he decides to let the first two gangsters go and shadow the one after that who is taller than all those who left before. What is the probability that the policeman will shadow the correct person? Answered by Steve La Rocque and Claude Tardif. 





What is the original cost? 
20060419 

From Charlie: Selling a piece of furniture for $670 and the profit is 35%. What is the original cost? Answered by Stephen La Rocque. 





What is the cost price? 
20060414 

From Purushotham: If the selling price is 120 and the profit is 20%, what is the cost price? Answered by Stephen La Rocque. 





Price percentages 
20060413 

From Kristine: An item that is no longer on sale at "25% off" receives a price tag that is 33 1/3% more than the sale price. Has the item price been restored to its original price? Why or Why not? Answered by Stephen La Rocque. 





List price plus 10% 
20060403 

From Heather: We shipped 2 pieces of an item with a unit price of $578.74 for a total amount of $1157.48. My task is to bill the customer at LIST + 10%. What formula do I need to use to calculate this? Answered by penny Nom. 





The square footage of an area in my backyard 
20060317 

From Kim: I need to find out how to calculate the square footage of an area in my backyard that is in the shape of a "slice of pie". There are two sides that are straight lines that come together at the top to form a point, and then at the bottom is a curved line that joins the two other lines together. I need to figure out how to calculate the square footage that is inside the area. Answered by Penny Nom. 





A probability question which resulted from a game of Yahtzee 
20051231 

From Robert: Could someone please assist me with this probability question which resulted from a game of Yahtzee we were playing in Melbourne, Australia on our holidays.
The object on this turn was to throw a “large straight” which is 5 numbers in sequence from 5 dice numbered 1 – 6. A player initially throws all 5 dice and then selects those dice they want to throw again for a further two more times. In this instance the player on their first throw, threw a 1,2,3,4 and 6.
Question: What is the respective probabilities of gaining a straight if they were to –
a) put back say the 6 and try and throw a 5 on the two further throws or…..
b) put back the 1 and 6 and try and throw a 1 and 5 or 5 and 6 on the two further throws bearing in mind that if one of the numbers was a 5 on the second throw they could hold that number and try for a 1 or 6 on the third throw.
I would be most appreciative if someone could assist in showing me how to calculate the probabilities particularly in the second instance (b). Answered by Penny Nom. 





Four 25sided dice 
20051124 

From dan: Simply put, I am curious to find the likelyhood of each possibility (4100) if I were to roll 4 25sided die. It seems to start off simply, as 1, 4, 10, 20...following the inside diagonal of Pascal's triangle. But as soon as i reach the point where the sum is greater than the number of sides, Pascal's no longer seems to work. I would be greatly appreciated if I could be informed of the proper formula to find this answer, or perhaps if my theory of doing it is wrong. Answered by Andrei Volodin and Shaun Fallat. 





I need to know the measurement of 75grams of spice into milliliters. 
20050916 

From Cyla: I don't know if this is possible but I need to know the measurement of 75grams of spice into milliliters. Even an approximation would be great. Answered by Penny Nom. 





Who is taller: John or Mary? 
20050914 

From Ulises: All the students in a school are arranged in a rectangular array. After that, the tallest student in each row was chosen, and then among these John Smith happened to be the shortest.Then, in each column, the shortest student was chosen, and Mary Brown was the tallest of these. Who is taller: John or Mary? Answered by Penny Nom and Claude Tardif. 





A melting ice sphere 
20050709 

From A student: A 2 meter diameter sphere of ice melts at 1.5 millimeters per minute. How many minutes will it take to fill up a hexagonal container measuring 1.5 meters on a side, and 0.8 meters deep? Answered by Penny Nom. 





Cost price 
20050525 

From Sunitha: What is (how to calculate) the cost price of a product which is markedup by 15% and retailed at $25? Answered by Penny Nom. 





A matrix problem 
20050404 

From Alan:
Let A = 

1  1  0 

2  1  2 
a  b  c 
where a, b, c are constant real numbers. For what values of a, b, c is A invertible? [Hint: Your answer should be an equation in a, b, c which satisfied if and only if A is invertible.]
Answered by Judi McDonald. 





Two matrix problems 
20050330 

From Sue: Question 1
Suppose all matrices in the equation below are square and invertible. Solve for x .
BA1XB1 + 2BA + In = 0 (the symbol "0" here denotes the matrix of all 0's in it)
Also, A1 or B1 is indicating inverse and "In" = for example, A1 times A
I hope you understand the above. I have to show all the steps.
Question 2
Suppose we consider the set of all 2x2 matrices along with the operations of matrix addition and multiplication. Do they form a field? Why or why not?
I think the answer is no because under multiplication it is not commutative and not all square matrices are invertible. I not positive so I'd like some help. Answered by Penny Nom. 





A matrix construction problem 
20050314 

From Marcelo: I want to know if is it possible to solve this problem:
I have an empty NxM matrix and I know totals (sum) by rows and totals by column.
Is there any algorithm to fill the matrix so that the summary of columns and rows gives the original values I have? Answered by Harley Weston. 





Strings of 4 digits from 1,2,...,7 
20041209 

From Tom: How many different combinations can be made of the numbers 17 in 4 string combinations in any order? EX:7235, 3517, etc...
And if you were to include the same 2 numbers in every combination, how many would that make? EX: Using 1 & 2: 1274, 5142, 2751, etc... Answered by Penny Nom. 





The price of a book 
20040918 

From Dorly: If the number of toonies required to buy a book is nine more than the number of
fivedollar bills required to buy the same book, determine the cost of the book. Answered by Penny. 





A pyramid 
20040511 

From Quiana: I am a student and I have the following questions I need to answer for homework:
How many sides, vertices, and edges does a pyramid have? Answered by Penny Nom. 





Three dice 
20040510 

From A student: If one has 3, 6 sided dice what is the probability of the numbers that are rolled to total 4 through 10 inclusively?
Subsequent to this, what is the probability to do this consecutively...say 3 times? Answered by Peny Nom. 





Arrays 
20040219 

From A parent: please demonstrate mathematical arrays fro a 3rd grader Answered by Penny Nom. 





Matrices 
20031205 

From Julie: I am doing a project and need to find some mathematiciens who had an influence in matrices. I can't seem to find any when I search online. Could you please help me with this? Answered by Judi McDonald. 





The mean house price 
20030910 

From Carol:
Question: I have to find the mean from the following example: Price Range £000  No of Houses  55 and under 60  3  60 and under 65  6  65 and under 70  13  70 and under 80  21  80 and under 100  15  100 and under 130  7  130 upwards  1  I know when calculating the mean you use the mid points of the classes, but how does this work for the 130 upwards class? Also, does this still work given the difference in the classes (ie. 1st class is 5, 5th class is 20, etc). Any help to get me started would be greatly appreciated. Answered by Penny Nom. 





An onsale DVD player 
20030709 

From Kim: I have a DVD player with a regular selling price of $175 and percentage of discount is 10 percent. How to solve for discount amount and sale price? Also, when you figure out the sale price how to figure out commission amount when percentage of commission is 5 percent? Answered by Penny Nom. 





8 faces, 12 vertices, and 18 edges 
20030422 

From Thomas: I would like to know the proper name for this geometrical solid. It has 8 faces, 12 vertices, and 18 edges? Answered by Penny Nom. 





A determinant 
20030213 

From A student:
I have to find the determinant of the following matrix 2  3  1  2  4  3  0  2  5  1  4  2  1  3  5  2  3  4  1  2  6  0  3  2  4  Answered by Penny Nom. 





A house's selling price 
20021105 

From Tanisha: a CERTAIN REALESTATE AGENT RECEIVES $6 FOR EVERY $100 OF A HOUSE'S SELLING PRICE. HOW MUCH WAS A HOUSE SOLD FOR IF THE AGENT $10,725._ Answered by Penny Nom. 





A sale price 
20021015 

From Chester: A jacket is on sale for 32% off. Find the original if the sale price is $89.00 Answered by Penny Nom. 





Tree diagrams 
20021012 

From Denean:
 For lunch, students can choose juice or milk; hamburger or pizza; and a banana or apple. How many lunch combinations can the students make?
 In an experiment, Monty can use paper towels or cloth. He can choose red, green, or yellow food coloring. How many combinations are there?
Answered by Penny Nom. 





A game of dice 
20020513 

From Mika: To play a game a dice is rolled to see who plays first. four players are going to play the game. what is the probability that at least two people roll the same number? ANSWER: P(least 2 people roll the same #)=number of player/total outcome P = 4!/4C2 = 24/4C2 = 4 the answer is 40% Answered by Andrei Volodin. 





A probability tree 
20020504 

From A student: Karl and Naomi roll three dice. Karl gives $10 to Naomi if the number 5 turns up once, twice or three times. Naomi gives Karl $3 in all other cases. A) construct the probability tree for this situation.
B) Does Karl have an advantage in this game? Justify your answer. My problem is I am unfamiliar on how to draw this probability tree and seem to be having a lot of difficulties, when you have a chance please answer this math problem and get back to me with the results. Answered by Penny Nom. 





If you conect all the vertices of a regular ngon... 
20020401 

From Murray: If you conect all the vertices of a regular ngon with lines you will have (n3)(n/2) lines inside the polygon. I want to find out how many sections these lines divide the polygon into and how many intersections they have with each other. Answered by Claude Tardif. 





Rolling 5 sevens before rolling a six or an eight 
20020120 

From Tony: When rolling 2 dice, what is the probability of rolling 5 sevens before rolling a six or an eight? Answered by Andrei Volodin and 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. 





Matrix 
20011121 

From Hoda: I have a question about matrix multiplication; well, actually, matrix division. I am assuming that matrices are divided the same as they are multiplied; that is, row by column. But what happens if you have to divide by zero? How does this affect the resulting matrix? Answered by Patrick Maidorn and Penny Nom. 





Free pamphlets 
20011024 

From Salman: a travel agency has limited number of six different free pamphlets about the beetle islands. the agent tells you to take any that you want, but not more than two of any kind. Assuming that you take at least one pamphlet, how many choices could you make Answered by Penny Nom. 





15 mice in 4 cages 
20011008 

From Chelsea: How can you fit 15 mice into 4 cages with an odd number of mice in each cage? Answered by Claude Tardif and Harley Weston. 





Rolling two dice 
20010910 

From Owen: This probability question has been bugging me for a while. Two ordinary dice are rolled. If it is known that one shows a 5, what is the probability that they total 8? I have two different but (seemingly) correct solutions. Answered by Andrei Volodin. 





Vertices 
20010808 

From Jordan: I am a fifth grader learning geometry with my mom's help, can you please explain what a vertices are?? Answered by Penny Nom. 





Conformable matrices 
20010805 

From Wayne: Can someone explain the concept of conformable matrices in a way that is easy to understand ? One definition says to multiply matrices rows and columns must conform, ie, 5 x 3 matrix times a 3 x 5 matrix. In the next example, however a 8 x 1 matrix and a 8 x 3 matrix are said to be conformable! Answered by Steve Kirkland. 





Matrix reconstruction 
20010719 

From Guy: Is there a way to get the sums of rows, columns and diagonals of an n x n matrix to reconstruct the original matrix? Answered by Walter Whiteley and Patrick Maidorn. 





Mutually exclusive 
20010605 

From Marje: What does the mathmatical term "mutually exclusive" mean. Pleas diagram if possible. Answered by Penny Nom. 





Probabilities and dice. 
20010504 

From Carmen: Hi! My name is Carmen! I am a member of a grade 5 class in Edmonton, AB. We were talking about probability in math, and I was wanted to know what the probability (odds) of rolling two sixes would be rolling two dice? If it is not to diffucult could you tell me what the probability (odds) of rolling any number with two dice were? Answered by Andrei Volodin and Penny Nom. 





Expected value 
20010424 

From Cindy: A game consists of rolling a single fair die. If a number great than 4 is rolled you win the number of dollars showing on the die. If any other number is rolled, you receive $1.00. What is the expected value of this game? Answered by Andrei Volodin. 





Oil revenue 
20010421 

From Brian: Suppose that t months from now an oil well will be producing crude oil at the rate of r(t), not a constant, barrels per month and that the price of crude oil will be p(t), not a constant, dollars per barrel. Assume that the oil is sold as soon as it is extracted from the ground.  Find an expression for the total revenue from the oil well, R(t).
 A certain oil well that currently yields 400 barrels of crude oil a month will run dry in 2 years. The price of crude oil is currently $18 per barrel and is expected to rise at a constant rate of 3 cents per barrel per month. What will be the total revenue from this well? {Hint: Model the degraded production rate with the equation:
r(t) = (ABt)e^{0.04t}} Answered by Harley Weston. 





Matrices 
20010326 

From Peg: What are some applications of matrices, basic trigonometry, and linear systems in the real world? I'm writing and Algebra report about where these topics are used outside of the classroom. Answered by Judi McDonald and Walter Whiteley. 





Solving Equations 
20010223 

From Stephanie: Do you know who came up with solving equations? Do you have any websites that can give me good information on solving equations? Do you know any history on solving equations? Do you know what solving equations is used for? And finally............Sorry about all of the questions :) Has the form of solving equations changed from the time it came out to now? Answered by Juci McDonald. 





Conditional probabiity 
20010122 

From Wallace Yang: A pair of sixsided fair dice is thrown. Find the probability that the sum is 10 or greater if it is given that a 5 appears on at least one of the dice. Answered by Penny Nom and Claude Tardif. 





The city transit system 
20010107 

From Jacky: The city transit system carries an average of 9450 bus riders a day, for a fare of $1.75 each. The city wants to reduce car pollution by increasing ridership and to maximize the transit system's revenue at the same time. A survey indicates that the number of riders will increase by 150 for every $0.05 decrease in fare. Answered by Harley Weston. 





Three dice 
20010103 

From John Read: I have three dice (A, B, C.) Three sides of each dice are blank. Three sides of each dice have a number. When the dice are thrown, it must be possible to result in the numbers 1 to 49 in any combinations without doubling up on any figure. i.e. Different combinations resulting in the same end number. I managed to get from 1 to 47 before getting stuck. Answered by Claude Tardif. 





Euler's Formula 
20001111 

From Denise Roberts: I'm trying to design a unit (possibly involving a Webquest) on Polyhedra and I cannot find a formula I once used. The formula involved the number of vertices (V), edges (E), and faces (F) of the polyhedra. Answered by Walter Whiteley. 





Where will we use this in the real world? 
20001011 

From Jane Ann Musgrove: As a teacher of mathematics, I am always asked "Where will we use this in the real world?". I am seeking ideas/sites via the internet where students can find answers to this type of question. Can you help me? To be more specific, right now I am interested in finding careers where the employees would use the concepts of "Radicals", "Matrices", and "Logarithms". This information will be used by students to make presentations to the class on their findings from internet searches. Answered by Harley Weston. 





Review problems 
20000918 

From Dee: A card is selected from an ordinary deck of cards. What is the probability of. . . selecting 2 aces in a row? If you toss two dice, what would be your probability of the following? . . . Answered by Penny Nom. 





A matrix equation 
20000514 

From A student: Right now, we are dealing with matrices and we are supposed to solve the following problem on our graphingcalculators: 2a+3b4c+d=20 a2b+3c5d=14 3a+4b2c+3d=19 5ab+6c+4d=5 Answered by Penny Nom. 





Matrices Information 
20000502 

From William Avery: I am an OAC student at Governor Simcoe Secondary School in St. Catharines Ontario. Today at school we were handed an independent study project by our Finite teacher. This assignment is based on Matrices, it involves performing some simple matrix calculations, but also involves a written section. This written section asks for the following: . . . Answered by Marley Weston. 





Taxis in Chicago 
20000327 

From A high school studenthigh school student: Suppose that taxis pick up and deliver passengers in Chicago, which is divided into three zones. Records kept by the drivers show that of the passengers picked up in Zone 1, 50% are taken to a destination in Zone 1, 40% to Zone 2, and 10% to Zone 3. OF the passengers picked up in Zone 2, 40% go to Zone 1, 30% to Zone 2, and 30% to Zone 3. Of the passengers picked up in Zone 3, 20% go to Zone 1, 60% to Zone 2 and 20% to Zone 3. Suppose that at the beginning of the day, 600 of the taxis are in Zone 1, 100 in Zone 2, and 300 in Zone 3. What is the distribution of taxis in the various zones after all have had two riders? Answered by Harley Weston. 





A Multiple Choice Test 
19990831 

From Cintra Ramnarine: I have ten questions. There are two multiple choice answers to each question. What are the chances of answering all questions correctly. Answered by Harley Weston. 





Matricies 
19981126 

From Stephanie Webster: If a matrix for a rectangle looks this way: AACC BDDB What does the matrix for a square look like? Answered by Penny Nom. 





Three dice 
19981117 

From Ryan Allinson: Rolling three regular dice how many different ways could a sum of 10 be rolled? Hope you can help. Can you please show me how this is done? Answered by Penny Nom. 





Snake Eyes 
19980720 

Would you please advise me what the probability is of rolling snake eyes on a pair of dice is? My recollection is 1 out of 6 multiplied by 1 out of 6 = 1 out of 36 is this correct? Answered by Jack LeSage and Penny Nom. 





Rolling a seven 
19980611 

From Bruce Thompson: What is the probablity of rolling two dice and it coming out as seven? a) 1/6 b) 1/36 please give me the correct awnser and explain please. Answered by Harley Weston. 





Mathematical Arrays 
19980501 

From Gene Lanctot: Could someone please explain what a mathematical or arithmetical array is? The array in question is used in grade three math in Ontario. I would also like to know what its purpose is. Answered by Harley Weston. 





Matrices 
19980310 

From Ksya:
 A and B are matrices. If A^n=B^n, can we say A=B or det(A)=det(B) or det(A)^n=det(B)^n ? Any conditions ???
 If B^(1) is the inverse of B, where B is a matrices. Can we say [(B^(1))^n][B^n]=I, where I is identity matrices? Any conditions???
Answered by Doug Farenick. 





Un bénéfice de 5% 
20080311 

From mahiques: Un propriétaire decide de vendre deux parcelles de terrains pour un montant total de 141750 F. Il fait un bénéfice de 15% sur la première et une perte de 10% sur la deuxième. L'ensemble de la transaction lui a rapporté un bénéfice de 5%.combien atil vendu chacune des parcelles ? Answered by PierreLouis Gagnon. 





exercices corrigés 
20070109 

From Zribi: si je peut avoir des exercice corrigé Answered by Claude Tardif. 





Matrice 
20060201 

From Kader: mon probleme est le suivant soit deux matrices carrees A et B d'ordre n qui sont anticommutatives AB= BA , demontrer que au moins une des deux matrices n'est pas inversible si n est impair.
je n'arrive pas a utiliser le fait que n soit impair, trouver le rapport entre n impair et inverse des matrices, je pars sur la base de DETAB=DETA*DETB Answered by Claude Tardif. 





probleme de matrice 
20060201 

From Un eleve: mon probleme est le suivant soit deux matrices carrees A et B d'ordre n qui sont anticommutatives AB= BA , demontrer que au moins une des deux matrices n'est pas inversible si n est impair. Answered by Claude Tardif. 





La bissectrice de l'angle ABC 
20000216 

From Laurent Gauthier: Estce redondant d'ecrire "angle ABC" avec un accent circonflexe sur le B? Peuton ou devraiton se contenter d'ecrire soit ABC (avec l'accent), soit l'angle ABC (sans accent) ? Le contexte dans lequel ceci apparait est le syntagme "la bissectrice de l'angle ABC", c'estadire que je me demande si on devrait ecrire "la bissectrice ABC " (avec accent), "la bissectrice de l'angle ABC" (sans accent) ou "la bissectrice de l'angle ABC" (avec accent). Answered by Claude Tardif. 

