Huy D. answered • 10/14/12

Experienced Math & CS Tutor

Hello Kirklin,

Most of the work here will be interpreting the problem and forming equations from the information given. Let's have it at step by step.

Store A: No matter what, you will be charged $18, so that needs to be in the equation. And then, you will be charged 2 cents, or $0.02 per copy. We don't know how many copies, so let's make that a variable called *x*. Then we get the equation:

A = 18 + 0.02x

So if you make one copy, it's $18.02, and if you make two copies, it's $18.04, and so on.

Store B: No matter what, you are charged $24, so that needs to be in the equation. And then, you will be charged 1.5 cents, or $0.015 per copy. We don't know how many copies, so let's make that a variable called *x*. Then we get the equation:

B = 24 + 0.015x

Once we have our two equations, we want both monthly costs to be the same. In other words, we want A = B, right?

A = B

Let's substitute in A:

18 + 0.02x = B

Now let's substitute in B:

18 + 0.02x = 24 + 0.015x

From here on it's algebra. Subtract 0.015x from both sides to get

18 + 0.005x = 24

Now subtract both sides by 18.

0.005x = 6

Dividing both sides by 0.005, we get:

x = 1200, or 1200 copies needed for the costs of store A and store B to be the same each month

________

Let's check our work

cost of A = 18 + 0.02 * 1200 = 18 + 24 = 42

cost of B = 24 + 0.015 * 1200 = 24 + 18 = 42

Both come out the same!