Question

The revenue for a vehicle rental store is $5460. There was 208 cars and 52 vans rented. A van rents for $10 more than a car.

a. Write a system of equations that represent this situation.

b. What is the cost of the car rental?

c.What is the cost of the van rental!

Answer 1

208c + 52v = 5460
v = c + 10

where c = the price for a car rental and v = the price for a van rental.
To solve this system, use substitution; the second equation says v is equal to c + 10, so plug in "c + 10" for v in the first equation and solve for c:

208c + 52(c + 10) = 5460
208c + 52c + 520 = 5460
260c + 520 = 5460
260c = 4940
c = 19

Now that we have c, we can plug it in to the second equation to find v:

v = (19) + 10
v = 29

So, c = 19 and v = 29, meaning that
The cost of a car rental is $19 and the cost of a van rental is $29.