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.
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.
1 answer