jon rented a car from a company that charged a daily rental fee and a mileage charge. He rented the car for 9 days and drove 300 miles and was charged $315. His friend Amanda later rented the same car for 5 days and drive 240 miles and was charged $186. What was the daily rental charge? How much did the company charge per mile?
let the daily rental fee be f
let the mileage charge be m
Jon: 9f + 300m = 315
3f + 100m = 105
Amanda: 5f + 240m = 186
jon x 5 -------> 15f + 500m = 525
Amanda x 3 ---> 15f + 720m = 558
subtract them:
220m = 33
m = 33/220 = 3/20 or .15
back into Jon
3f + 100(.15) = 105
f = 30
They charged $30 per day, plus 15 cents per mile
To find the daily rental charge and the mileage charge, we can set up a system of equations. Let's use variables for the daily rental charge (r) and the mileage charge per mile (m).
For Jon's rental:
Daily rental fee * Number of days + Mileage charge per mile * Number of miles = Total charge
r * 9 + m * 300 = 315
For Amanda's rental:
Daily rental fee * Number of days + Mileage charge per mile * Number of miles = Total charge
r * 5 + m * 240 = 186
Now we can solve this system of equations to find the values of r and m.
To do that, we can use the method of elimination. Multiply the first equation by 5 and the second equation by 9 to eliminate the daily rental fee (r).
5(r * 9 + m * 300) = 5(315)
9(r * 5 + m * 240) = 9(186)
Simplifying the equations:
45r + 1500m = 1575
45r + 2160m = 1674
Now subtract the second equation from the first equation:
(45r + 1500m) - (45r + 2160m) = 1575 - 1674
Simplifying:
-660m = -99
Divide both sides by -660:
m = -99 / -660
m = 0.15
Now substitute the value of m into either of the original equations to find the daily rental fee (r). Let's use the first equation:
r * 9 + 0.15 * 300 = 315
Simplifying:
9r + 45 = 315
9r = 315 - 45
9r = 270
Divide both sides by 9:
r = 270 / 9
r = 30
So, the daily rental charge is $30, and the company charges $0.15 per mile.