Question

A copy center offers its customers two different pricing plans for black and white photocopies of 8.5 in by 11 in. pages. Customers can either pay $0.08 per page or pay $7. 50 for a discount card that lowers the cost to S0.05 per page. Write and solve an equation to find the number of phe which the cost of each plan is the same.

Answer 1

To determine the point at which the cost of both pricing plans is the same, we can set up and solve an equation.

Let's define \( x \) as the number of pages copied.

For the first plan (pay-as-you-go):
- The cost per page is $0.08, so the total cost \( C_1 \) is given by:
\[
C_1 = 0.08x
\]

For the second plan (discount card):
- There is an upfront cost of $7.50 for the card, and each page then costs $0.05. Thus, the total cost \( C_2 \) is given by:
\[
C_2 = 7.50 + 0.05x
\]

We need to determine the number of pages \( x \) for which the total costs are the same:
\[
C_1 = C_2
\]
Substituting the expressions for \( C_1 \) and \( C_2 \) gives:
\[
0.08x = 7.50 + 0.05x
\]

To solve for \( x \), first isolate the variable term on one side of the equation. Subtract \( 0.05x \) from both sides:
\[
0.08x - 0.05x = 7.50
\]

Simplify the left side:
\[
0.03x = 7.50
\]

Now, solve for \( x \) by dividing both sides by 0.03:
\[
x = \frac{7.50}{0.03} = 250
\]

Thus, the number of pages at which the cost of each plan is the same is \( x = 250 \) pages.