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.

the daily fee is 37 and the mileage charge is .24 per mile.
Step-by-step 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.