Question

Suzanne is going to rent a car while she is out of town. One car rental company offers a flat rate of $35 per day plus $0.10 per mile. Another car rental company offers the same car for $25 per day plus $0.25 per mile. She will need the car for 5 days. How many miles would she need to drive for the first rental company to be a better deal?

Answer 1

She need to drive more than 2000 miles for the first rental company to be a better deal .

Explanation:

Case 1) One car rental company offers a flat rate of $35 per day plus $0.10 per mile

Let m be the no. of miles

She will need the car for 5 days.

So, total cost =
`35 * 5 +0.10m=175+0.10m`

Case 2) Another car rental company offers the same car for $25 per day plus $0.25 per mile.

Let m be the no. of miles

She will need the car for 5 days.

So, total cost =
`25 * 5 +0.25m=125 +0.25m`

Now we are supposed to find How many miles would she need to drive for the first rental company to be a better deal?

So,
`175+0.10m <125 +0.25m`

`175+125 <125 +0.25m-0.10m`

`300 < 0.15m`

`(300)/(0.15) < m`

`2000 < m`

So, she need to drive more than 2000 miles for the first rental company to be a better deal

Answer 2

r1 = 35*d + .10*m, rental car company 1r2 = 25*d + .25m, rental car company 2
r1 will be a better deal when when r2 > r1r2 > r1 when35*5 + .10*m > 25*5 + .25m5(35-25) > (.25 - .10)m5*10 > (.15)m50/.15 > mm > 50/.15 = 33 1/3
Ans. When 33 1/3 miles have been driven, rental car company r1 will be a better deal.