Question

All will rent a for the weekend. He can choose one of two plan has an 53.96 and costs an additionalper mile driven second plan fee of $57.96 and costs an additional per mile driven. How miles would All need to drive the two plans to cost the same?

Answer 1

Let the miles driven be x;

Let the cost of the plan be c;

The first plan costs (in dollars);

`c=53.96+0.13x`

Then, the second plan costs (in dollars);

`c=57.96+0.11x`

When the costs are same, we have;

`53.96+0.13x=57.96+0.11x`

Simplifying further by collecting like terms, we have;

`\begin{gathered} 0.13x-0.11x=57.96-53.96 \\ 0.02x=4 \\ x=(4)/(0.02) \\ x=200 \end{gathered}`

The miles Ali need to drive so the two plans cost the same is 200 miles.