Question

Charlie’s Car Rentals charges a flat fee of $20 plus $24/day to rent a car. Jerry’s Car Rentals charges $28/day with no flat fee. The system that models this situation is given, where c is the cost of renting a car and d is the number of days a car is rented.

c = 20 + 24d
c = 28d

The solution to the system is (5, 140).

Which interpretation correctly describes the solution to the system of equations?


A.
The cost to rent a car is the same, $140, for both car rental companies if you rent a car for 5 days.

B.
The cost to rent a car is the same, $5, for both car rental companies if you rent a car for 140 days.

C.
Company A will charge more money on the fifth day by charging $140.

D.
Company A will charge less money on the fifth day by charging $140.

Answer 1

The answer is A.

If you imagine these two equation to model the price of renting from either company:
c = 20 + 24d (Charlie's)
c = 28d (Jerry's)

c represents the cost as a function of d, which represents the days.
At d = 5, both equations are 140

We can see this if we plug in 5 for d in both equations.
20 + 24(5) = 140 and 28(5) = 140

This means the data point (5, 140) which represents 5 days with a cost of $140 satisfies both equations and is the solution to the system of equations.

Therefore, the answer is A.

Answer 2

A is correct because if you subsitute 5 for d or days, you get 140 for both equations

B is obviously wrong because a positive number of days +20 is not more than 5 for charlie's car rentals

C is wrong because we saw that in 5 days, the car companies earn equal ammounts

D is wrong because we saw that in 5 days, the car companies earn equal ammounts