A rental car company charges an upfront fee to rent a car, and then charges $0.40 per mile driven. It will cost you $60 to drive 50 miles. Suppose you rent a car from this company.

Question

A rental car company charges an upfront fee to rent a car, and then charges $0.40 per mile driven. It will cost you $60 to drive 50 miles. Suppose you rent a car from this company.

Suppose the number of miles you drive in the rental car changes from 50 miles to 110 miles.

1. 
   
2. What is the corresponding change in the number of miles you drove in the rental car?
3. 
   
4. What is the corresponding change in the total price (in dollars) you must pay for the rental car?
5. What is the total cost of the rental car (in dollars) if you drive 110 miles in the car?
6. 
   
7. 
   
8. 
   

Answer 1

The change in the number of miles driven from 50 miles to 110 miles is:

110 miles - 50 miles = 60 miles

The corresponding change in price:

Since it costs $0.40 per mile, 60 miles would cost:

$0.40 * 60 = $24

If it cost $60 to go 50 miles, including the upfront fee, the extra cost for the extra miles would just be added to this cost:

$60 + $24 = $84

Answer 2

Let C be the cost of the rental, F be the fee they charge up front, and m be the number of miles driven. The equation modeling this situation is then C = 0.4m + F. To determine what F is, use the information given that it will cost $60 to drive 50 miles. So 60 = 0.4(50) + F or F = 40. The equation modeling the situation now becomes C = 0.4m + 40.

What is the corresponding change in the number of miles you drove in the rental car?

You drove from 50 miles to 110 miles so the change in miles is 110 - 50 = 60 miles

What is the corresponding change in the total price (in dollars) you must pay for the rental car?

The change in price is given by plugging in the 60 miles into the modeling equation so C = 0.4(60) + 40 = $64

What is the total cost of the rental car (in dollars) if you drive 110 miles in the car?

The total cost is the original $60 plus the new $64 or $124