Question

1. ccss reason abstractly each game at a carnival costs $0.50, or you can pay $15 and play an unlimited amount of games. write and solve an inequality to find how many times you should play a game so that the unlimited game play is less expensive than paying each time. interpret the solution.

inequality:
solution:
interpretation:

Explanation:

Step1: Define variable and inequality

Let \( x \) be the number of games played. The cost of paying per game is \( 0.50x \), and the unlimited play cost is \( 15 \). We want when unlimited is cheaper: \( 0.50x > 15 \).

Step2: Solve the inequality

Divide both sides by \( 0.50 \): \( x > \frac{15}{0.50} = 30 \).

Step3: Interpret the solution

\( x > 30 \) means playing more than 30 games makes unlimited play cheaper.

Answer:

Inequality: \( 0.50x > 15 \)
Solution: \( x > 30 \)
Interpretation: If you play more than 30 games, paying $15 for unlimited play is less expensive than paying $0.50 per game.