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 $244.50 On her second business trip she drove 200 miles in 3​ days, and paid $149.00

for the rental. Find the daily​ fee, and find the mileage charge.

Answer 1

Using a system of equations and the method of elimination, the daily fee for the car rental is determined to be $33.00 and the mileage charge is $0.25 per mile.

Step-by-step explanation:

To find the daily fee and the mileage charge from the car rental company, we need to set up a system of equations based on the information provided:

1. Judy's first trip cost: $244.50 for 4 days and 450 miles
2. Judy's second trip cost: $149.00 for 3 days and 200 miles

Let's define two variables, D for the daily fee and M for the mileage charge per mile. We can write two equations based on the given information:

1. 4D + 450M = $244.50 (First trip)
2. 3D + 200M = $149.00 (Second trip)

Now we'll solve this system using substitution or elimination. Using elimination, we multiply the second equation by 4 and the first by 3 to cancel out D when we subtract them:

• (3)(4D + 450M) = 3($244.50)
• (4)(3D + 200M) = 4($149.00)

Subtracting these equations we get:

• 12D + 1350M = $733.50
• 12D + 800M = $596.00
• --------------------------
• 0D + 550M = $137.50

Dividing by 550, we find the mileage charge: M = $0.25 per mile.

Now we plug the value of M into one of the original equations to find D:

1. 3D + 200(0.25) = $149.00
2. 3D + $50 = $149.00
3. 3D = $99.00
4. D = $33.00

The daily fee is $33.00.