Question

A car rental company has two rental rates. Rate 1 is $81 per day plus $0.18 per mile. Rate 2 is $162 per day plus $0.09 per mile. If you plan to rent for one day, what is the least number of miles above which you would pay less by taking Rate 2?

Answer 1

The least number of miles above which you would pay less by taking Rate 2 is 900 miles.

Explanation:

A car rental company has two rental rates.

Rate 1 :

Rental per day =$81

Cost per mile = $0.18

Cost for x miles = $0.18x

Total cost for x miles for 1 day=81+0.18x

Rate 2:

Rental per day =$162

Cost per mile = $0.09

Cost for x miles = $0.09x

Total cost for x miles for 1 day=162+0.09x

We are supposed to find what is the least number of miles above which you would pay less by taking Rate 2

`81+0.18x>162+0.09x\\0.18x-0.09x>162-81\\0.09x>81\\x>(81)/(0.09)\\x>900`

Hence the least number of miles above which you would pay less by taking Rate 2 is 900 miles.