Question

1. 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

Let \( x \) be the number of games played.

Step2: Set up inequality

Paying per game: total cost is \( 0.50x \). Unlimited play cost: \( 15 \). We want unlimited play less expensive: \( 0.50x > 15 \).

Step3: Solve inequality

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

Step4: Interpret solution

\( x > 30 \) means when playing more than 30 games, unlimited play (\$15) is cheaper than paying \$0.50 per game.

Answer:

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