Question

Penny's parents gave her $50 to spend on new video games. Used games are $7 and new games are $12. Part 1: What is the system of inequalities that represent this situation? Part 2: What is the maximum amount of used games that she could buy? Part 3: What are the minimum amount of new games that she could buy? Part 4: What are two possible combinations of used and new games she can purchase?

Answer 1

The correct answers are Part 1: 7x + 12y
`\leq` 50, x,y
`\geq` 0; Part 2: 7; Part 3: 0: Part 4: 2 old and 3 new video games.

Explanation:

Penny's parents gave her $50 to buy new video games.

Price of used games are $7 and new games are $12.

Let Penny buy x number of old video games and y number of new video games.

Part 1:

Total price she spent on buying the video games are 7x + 12y.

This amount should be less than or equal to the amount of money she possess. therefore 7x + 12y
`\leq` 50, x, y
`\geq` 0.

Part 2:

Maximum number of used game she can buy can be given when she spends all her money just on used games. Therefore y = 0. This implies x
`\leq (50)/(7)`.

Thus the maximum number of used game she can buy is 7 where she does not buy any new game and has $1 left with her after the purchase.

Part 3:

Minimum number of new games that Penny can buy is zero. She can not buy any new games and spent all her money purchasing old games.

Part 4:

The possible combination in which she can purchase both the video games is 2 old games and 3 new games.