Question

dan will rent a car for the weekend. he can choose one of two plans. the forat plan has an initial fee of $59.98 and costs an additional $0.10 per mile driven the second plan has an initial fee of $55.98 and costs an additional $0.15 per mile driven. how many miles would dan need to drive for two plans to cost the same?

Answer 1

Let:

y1 = Total cost of forat plan

y2 = Total cost of second plan

x = Number of miles

a1 = Cost per mile of forat plan

a2 = Cost per mile of the second plan

b1 = Initial fee of forat plan

b2 = Initial fee of the second plan

The total cost for every plan is given by:

$\begin{gathered} y1=a1x+b1 \\ y2=a2x+b2 \\ _{\text{ }}where\colon \\ a1=0.1 \\ a2=0.15 \\ b1=59.98 \\ b2=55.98 \\ so\colon \\ y1=0.1x+59.98 \\ y2=0.15x+55.98 \end{gathered}$

We need to know:

$\begin{gathered} y1=y2 \\ 0.1x+59.98=0.15x+55.98 \\ \end{gathered}$

Solve for x:

$\begin{gathered} 59.98-55.98=0.15x-0.1x \\ 4=0.05x \\ x=\frac{4}{0.05} \\ x=80 \end{gathered}$

Answer:

80 mi