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

Question

This problem has three parts. 

 

Part A asks for a system of equations that represent this situation.

Part B asks for the cost of a car rental

Part C asks for the cost of a van rental

Answer 1

Hi Jillian,

 

So lets start off with the information that we were given. 

 

We know that 208 cars were rented and that 52 vans were rented.

 

The total cost of renting 208 cars and 52 vans is 5460.

 

We are told that a van costs $10 more to rent than a car.

 

What we don't know is how much it costs to rent a van and how much it costs to rent a car. We represent these unknown quantities with variables.

 

Let's say that it costs X dollars to rent a car and Y dollars to rent a van.

 

To rent 208 cars it would cost 208X

 

To rent 52 vans it would cost 52Y    And we know that both of these added together costs 5460.

 

The equation that would represent this is  208X + 52Y = 5460

 

We were told that vans cost 10 more than cars. The equation for this relationship is Y = X + 10 or Y - X = 10

 

Part A is those two equations

 

208X + 52Y = 5460

Y - X = 10

 

For parts B and C, we need to solve for x and y.

 

We can accomplish this by substitution. We know that Y = X + 10 so we will substitute X + 10 for Y in the first equation. It looks like this:

 

208X + 52[X + 10] = 5460

 

Then we want to expand 52[X + 10] into 52X + 520

 

This gives us 208X + 52X + 520 = 5460  when we simplify it becomes 260X = 4940... then we divide both sides by 260 to give us X = 19

 

So it costs 19 dollars to rent a car.

 

It costs 10 more to rent a van.... Y = X + 10... Y = 19 + 10 = 29

 

So it costs 29 to rent a van

 

Hope this helped