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
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!