Question

Ahmad will rent a car for the weekend. he can choose one choose one of two plans. the first plan has an initial fee of $55 and cost an additional $0.13 per mile driven the second plan has an initial fee of $48 and cost am additional $0.17 per mile driven

Answer 1

(a) The first plan cost $55 and an additional $0.13 per mile driven,

while the second plan cost $48 and an additional $0.17 per mile driven

Let the amount of driving be x

Then, this means that for the first plan we have

`\begin{gathered} 55+(0.13* x) \\ =55+0.13x \end{gathered}`

And the second plan becomes

`\begin{gathered} 48+(0.17* x) \\ =48+0.17x \end{gathered}`

So, for the plans to cost the same for a particular amount of driving x, it means that

`55+0.13x=48+0.17x`

Collecting like terms we have

`\begin{gathered} 55-48=0.17x-0.13x \\ 7=0.04x \\ x=(7)/(0.04) \\ x=175 \end{gathered}`

Hence the two plans cost the same at 175 miles

(b) The cost when the two plans cost the same is

`\begin{gathered} 55+0.13x \\ 55+0.13(175) \\ =55+22.75=77.75 \\ Or\text{ } \\ 48+0.17x \\ =48+0.17(175) \\ =48+29.75=77.75 \end{gathered}`

Hence the answer is $77.75