linear equations

Question

store A charges $18 per month plus 2 cents per copy. Store B charges $24 plus 1.5 cents per copy. How many copies need to be made for the monthly costs of both plans to be the same

Answer 1

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!

Answer 2

Hi, Lisa.

Store A charges $18 per month plus 2 cents per copy. The number of copies is our variable, so we can make this into an equation:

A = 18 + .02n     where n is the number of copies. It's .02n because the cost per copy is in cents and the 18 is dollars.

Store B:

B = 24 + .015n

We want to find the number of copies that makes these plans cost the same, so we set the expressions equal to each other and solve for n:

   18 + .02n = 24 + .015n
  -18             -18          

          .02n =   6 + .015n
         -.015n        -.015n

          .005n = 6  
          .005    .005   

            n = 1200 copies

We can easily check this by putting 1200 back into the equations for A & B:

A = 18 + .02(1200) = 42

B = 24 + .015(1200) = 42

They are equal, so our solution is 1200 copies.

Hope this helps!