Question

Kira will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $40 and costs an additional $0.30 per mile driven. The second plan has no initial fee but costs $0.80 per mile driven.

Answer 1

Given: Two rents plans and the costs

To Determine: The miles traveled when the two plans cost the same and the cost when the two plans cost the same

Solution: Let the total miles covered for each plan be

The cost of the first plan would be

$C_{ost\text{ of the plan A}}=40+0.30x$

The cost of the second plan would be

$C_{ost\text{ of thesecond plan}}=0.80x$

If the two cost is the same, then

$0.80x=40+0.30x$

Solve for x by collecting like terms

$\begin{gathered} 0.80x-0.30x=40 \\ 0.50x=40 \\ x=\frac{40}{0.5} \\ x=80 \end{gathered}$

The cost when the two plans cost the same would be

$\begin{gathered} 0.80x=0.80\times80=64 \\ Or \\ 40+0.30x=40+0.30\times80=40+24=64 \end{gathered}$

Hence, the miles covered when the plans cost the same is 80 miles

The cost when the two plans cost the same is $64