Question

Laura will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $55.98 and costs an additional $0.13 per mile driven.

The second plan has an initial fee of $69.98 and costs an additional $0.08 per mile driven. How many miles would Laura need to drive for the two plans to cost
the same?

Answer 1

Answer: it would take 280 miles before Laura pays the same amount for both plans..

Explanation:

Let x represent the number of miles that Laura drives using either the first plan or the second plan

Let y represent the total cost of x miles when using the first plan

Let y represent the total cost of x miles when using the second plan

The first plan has an initial fee of $55.98 and costs an additional $0.13 per mile driven. This means that the total cost of x miles would be

y = 0.13x + 55.98

The second plan has an initial fee of $69.98 and costs an additional $0.08 per mile driven.This means that the total cost of x miles would be

z = 0.08x + 69.98

To determine the number of miles that Laura would drive before the amount for both plans becomes the same, we would equate y to z. It becomes

0.13x + 55.98 = 0.08x + 69.98

0.13x - 0.08x = 69.98 - 55.98

0.05x = 14

x = 280