Question

Twice last month, Judy Carter rented a car from a car rental company and traveled around the Southwest on business. The company rents its car for a daily fee, plus an

additional charge per mile driven. Judy recalls that her first trip lasted 4 days, she drove 450 miles, and the rental cost her $256.00. On her second business trip she drove
200 miles in 3 days, and paid $159.00 for the rental. Find the daily fee, and find the mileage charge.

Answer 1

the daily fee is 37 and the mileage charge is .24 per mile.

Explanation:

256 = 450x + 4b

159 = 200x + 3b

Multiple the top equations by -3 all the way through the bottom equations by 4 all the way through then add the equation together.

-768 = -1350x -12b

636 = 800x + 12b

-132 = -550x Divide both sides by -550

.24 = x This is the charge per mile.

Plug in .24 for x into either of the original 2 equations to solve for b which is the daily fee.

256 = 450(.24) = 4b

256 = 108 + 4b Subtract 108 from both sides

148 = 4b Divide both sides by 4

37 = b This is the daily fee.