Question

Primo car rental agency charges 32 per day plus 0.10 per mile. Ultimo car rental agency charges 26 per day plus 0.65 per mile. Find the daily mileage for which the Ultimo charge is three times the Primo charge.

Answer 1

Let x be the dayly mileage used.

Primo car charges $32 per day plus $0.10 per mile, then the cost for x miles is:

`0.10x+32`

Ultimo car charges $26 per day and $0.65 per mile, then the total cost for x miles is:

`\text{0}.65x+26`

We want to know for how many miles ultimo charges three times as much as primo, then we have the equation:

`0.65x+26=3(0.10x+32)`

Solving for x we have:

`\begin{gathered} 0.65x+26=3(0.10x+32) \\ 0.65x+26=0.30x+96 \\ 0.65x-0.30x=96-26 \\ 0.35x=70 \\ x=(70)/(0.35) \\ x=200 \end{gathered}`

Therefore for 200 miles ultimo charges three times as much as primo.