Question

One month Tammy rented 2 movies and 3 video games for a total of $25. The next month she rented 4 movies and 8 video games for a total of $61. Find the

rental cost for each movie and each video game.

Answer 1

cost of each video game = $5.50

cost of each movie = $4.25.

Explanation:

Let m represent cost per movie

g represents cost per video game.

Create two equations to represent the total cost Tammy rented movie and video games in each month, and solve simultaneously for each variable:

First month:

`2m + 3g = 25` => equation 1

Second month:

`4m + 8g = 61` => equation 2

Multiply equation 1 by 4, and multiply equation 2 by 2 to derive:

4 ×
`2m + 3g = 25`

2 ×
`4m + 8g = 61`

`8m + 12g = 100` => equation 3

`8m + 16g = 122` => equation 4

Subtract equation 4 from equation 3

You'd have:

- 4g = - 22

Divide both sides by -4

g = 5.5

Thus, the cost of each video game = $5.50.

Substitute g = 5.5 in equation 1 and solve for m.

`2m + 3g = 25`

`2m + 3(5.5) = 25`

`2m + 16.5 = 25`

Subtract 16.5 from each side

`2m = 25 - 16.5`

`2m = 8.5`

Divide both sides by 2

`m = 4.25`

Thus, cost of each movie = $4.25.