Question

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

Answer 1

The correct answers are Part 1: 7x + 12y 50, x,y 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 50, x, y 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 .

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.

hope this helps