Question

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

Answer 1

To make the unlimited game play a better deal than paying per game, you should play more than 30 games.

Step-by-step explanation:

To determine when the unlimited pass becomes cheaper than paying per game, set up an inequality. Le t
`\(x\)` represent the number of games played.

For paying per game: Cost per game = $0.50. So, the cost for
`\(x\)` games =
`\(0.50x\)` .

For the unlimited pass: Cost = $15 regardless of the number of games played.

To find when the unlimited pass is cheaper, set up the inequality:
`\(0.50x > 15\)` .

Solve for
`\(x\)` :

`\[0.50x > 15\]`

`\[x > (15)/(0.50)\]`

`\[x > 30\]`

Thus, playing more than 30 games makes the unlimited pass a better deal than paying per game.

In simpler terms, if you play more than 30 games, the total cost of paying $0.50 per game surpasses the fixed cost of $15 for the unlimited pass. Opting for the unlimited pass becomes more cost-effective beyond this threshold. Therefore, if you plan to play more than 30 games, the unlimited pass is the more economical choice.