Question

nicole will rent a car for the weekend. she can choose one of two plans. the first plan has an initial fee of $45.96 and costs an additional $0.15 per mile driven. the second plan has an initial fee of $53.96 and costs an additional $0.13 per mile driven. how many miles would nicole need to drive for the two plans to cost the same? miles

Explanation:

Step1: Define variables and cost functions

Let \( x \) be the number of miles driven. The cost of the first plan \( C_1 \) is \( C_1 = 45.96 + 0.15x \). The cost of the second plan \( C_2 \) is \( C_2 = 53.96 + 0.13x \).

Step2: Set costs equal and solve for \( x \)

Set \( C_1 = C_2 \):
\( 45.96 + 0.15x = 53.96 + 0.13x \)
Subtract \( 0.13x \) from both sides:
\( 45.96 + 0.02x = 53.96 \)
Subtract \( 45.96 \) from both sides:
\( 0.02x = 8 \)
Divide both sides by \( 0.02 \):
\( x = \frac{8}{0.02} = 400 \)

Answer:

400