Question

Photocopying. Quick Copy recently charged 49¢ per page for color copies and 7¢ per page for black-and-white copies. If Shirlee’s bill for 90 copies was $11.34, how many copies of each type were made?

Answer 1

Make the number of color copies x and the number of bw copies y

0.49x + 0.07y = 11.34 and
x + y = 90

Then you can solve this system of equations in a variety of ways.

Answer 2

Ok what i did was take .49*90 and 0.07 *90 am i wrong?

Answer 3

Yes, because there were 90 copies all together. What you did was multiply 49 cents by 90 copies and 7 cents by 90 copies which would be 180 copies all together.

Answer 4

uhhh im so frustrated sorry

Answer 5

Not a problem. Can you see what I did at the start where I made the equations?

Answer 6

yes

Answer 7

You don't know how many color and bw copies there were, so they are unknowns. You can assign them a variable each.

Answer 8

The information that you're given enables you to make two equations. One equation results in the total cost and the other results in the total number of copies.

Answer 9

Now, you need to figure out x and y (the number of color and bw copies) are.

Answer 10

thats where im confused lol

Answer 11

A simple method for doing that is to isolate one of the variables in one of the equations like this:

x + y = 90
if x + y = 90, then 90 - y = x, and 90 - x = y same as any fact family like:

2 + 3 = 5, so 5 - 2 = 3 and 5 - 3 = 2

Answer 12

So using that information, you know that x = 90 - y (you could also use y=90-x, but you have to make choices sometimes).

This is where the other equation comes in. The other equation is:

0.49x + 0.07y = 11.34

We can substitute the value of x we found from the first equation (x=90-y) into where x is in the second equation like this:

0.49(90-y) + 0.07y = 11.34

Answer 13

Now, you need to multiply through the 0.49(90-y) part to get 44.1 - 0.49y and the equation is now:

44.1 - 0.49y + 0.07y = 11.34

Answer 14

You can group together the like terms. The terms with the y's are like and the terms with no variables are like.

Problem is, the two terms without variables are on different sides of the equation. If you move a term from one side of an equation to the other side, you need to change the sign. So, moving the 11.34 from the right side to the left side makes it -11.34

Answer 15

44.1 - 11.34 - 0.42y = 0

I combined the y terms (-0.49+0.07=-0.42). And since there was nothing left on the right side after moving over the 11.34, it is now equal to 0.

Answer 16

Following so far?

Answer 17

Now, I'll combine the 44.1 and -11.34 to get 32.76.

The y term needs to be by itself on one side of the equation, so I'll move it to the right side (don't forget to change the sign, and now we have:

32.76 = 0.42y

The final step is to divide both sides of the equation by 0.42, so you end up with a single y on the right side.

32.76/0.42=0.42y/0.42

which results in 78 = y or y = 78

Answer 18

If you remember way back, y was the number of black and white copies, and if you added the number of bw copies and the number of color copies, you'd get 90 all together. The number of color copies must be 90 - 78 = 12.

You can also check your answer by using those numbers in the other equation to see if you end up with $11.34.

Cheers!