Question

One week Timothy rented 4 DVDs and 2 video games for $22. The next week he rented 2 DVDs and 4 video game for $29 . Find the rental cost for a video game.

Answer 1

To find the rental cost for a video game, we set up a system of equations based on the given rental scenarios and solved it. We determined that the cost to rent one video game is $6.

Step-by-step explanation:

The student's question deals with a system of linear equations, which can be used to determine the cost of renting DVDs and video games. Let's denote the cost of renting one DVD as D and the cost of renting one video game as V. We are given two scenarios:

• 4 DVDs and 2 video games for $22: 4D + 2V = 22
• 2 DVDs and 4 video games for $29: 2D + 4V = 29

To find the cost of renting a video game, we can solve this system of equations. Multiplying the first equation by 0.5 to match the coefficient of D in the second equation gives us:

• 2D + V = 11

Subtracting this from the second equation, 2D + 4V = 29, gives:

• 3V = 18

Dividing by 3 on both sides to solve for V, we get:

• V = 6

Therefore, the rental cost for one video game is $6.