Q. A rental car agency charges $30 per day plus 10 cents per mile to rent a certain car. Another agency charges $20 per day plus 15 cents per mile to rent the same car. If the car is rented for one day in how many miles will the charge from both agencies be equal?
A. Recall: 10 cents = 0.1$, 15 cents = 0.15$
If you rent a car from the first car agency your cost for the rental will be:
(1)
If you rent a car from the second car agency the total amount of money to pay is:
(2)
Given that the problem says you want to rent the car just for one day, then D = 1, therefore:
First agency:
Second agency:
At some number of miles driven the two costs will be the same:
Solving for M:
There is a representation of this problem in figure 4. Up until you drive 200 miles you would save money by going with the second company.