Question

A certain video rental store rents video games for $4.99 and movies for $2.99. One day the store rented a total of 35 video games and movies. If the total rental income for this day was $144.65, not including tax, which of the following statements is a reasonable conclusion?

A) They rented 10 video games and 25 movies.
B) They rented 5 video games and 30 movies.
C) They rented 20 video games and 15 movies.
D) They rented 15 video games and 20 movies.

Answer 1

After setting up a system of equations with x representing the number of video games and y representing the number of movies, we solve the equations to conclude that the store rented 20 video games and 15 movies.

Step-by-step explanation:

To solve the question about the number of video games and movies rented, we need to set up a system of equations based on the given information. Let's denote the number of video games rented as x and the number of movies rented as y.

We are given two equations based on the problem statement:

1. The total number of items rented: x + y = 35

2. The total rental income: 4.99x + 2.99y = 144.65

Now let's solve the system of equations. We can start by multiplying the second equation by 100 to get rid of decimals:

499x + 299y = 14465

Using the first equation to express y in terms of x (y = 35 - x) and plugging it into the adjusted second equation, we get:

499x + 299(35 - x) = 14465

This simplifies to:

499x + 10465 - 299x = 14465

Combining like terms gives us:

200x = 4000

And solving for x:

x = 20

Using x to find y, we have:

y = 35 - 20 = 15

So the store rented 20 video games and 15 movies, corresponding to option C.