Question

Wayne has $80.00 to spend on video games. Used video games cost $10.00 each and new video games cost $20.00 each. This situation can be explained by using the equation (in standard form): 10x + 20y = 80. What does the variable x represent in this equation?

A) The cost of new video games
B) The total amount of money Wayne has
C) The cost of used video games
D) The number of video games Wayne can buy

Answer 1

In the equation 10x + 20y = 80, the variable x represents the number of used video games Wayne can buy at $10 each within his $80 budget.

Step-by-step explanation:

The equation presented in the question is 10x + 20y = 80, which is used to determine how Wayne can spend his $80 on video games. In this equation, the variable x represents the number of used video games Wayne can buy, each costing $10. On the other hand, the variable y represents the number of new video games Wayne can buy, with each new game costing $20. This setup allows us to calculate different combinations of new and used video games that Wayne can purchase within his budget of $80.

For example, if he buys only used games (x), he could purchase 8 of them (since 10x = 80, x = 8), or if he prefers only new games (y), he could buy 4 (because 20y = 80, y = 4). The equation in the standard form helps us assess these scenarios by balancing the cost per game with the total amount of money available.