Question

1. at the balloon dart booth, players are charged $1 for the chance to throw 3 darts. prizes worth $4 each are awarded to players who pop at least 2 balloons. last year, 4 out of 12 players popped 2 balloons, and 1 out of 12 players popped 3 balloons.

a. if the ratio of winners to players is the same this year and 204 people play the game, how much money will the booth earn or lose? explain.

Explanation:

Step1: Find the number of winners last year

Last year, 4 out of 12 popped 2 balloons and 1 out of 12 popped 3 balloons. So total winners = 4 + 1 = 5. The ratio of winners to players is $\frac{5}{12}$.

Step2: Find the number of winners this year

This year, there are 204 players. Let the number of winners be $x$. Using the ratio $\frac{x}{204}=\frac{5}{12}$. Cross - multiply: $12x = 204\times5$. $12x = 1020$. Then $x=\frac{1020}{12}=85$.

Step3: Calculate total revenue and total prize cost

• Total revenue: Each player pays $1, so for 204 players, revenue = $204\times1=\$204$.
• Total prize cost: Each prize is $4, and there are 85 winners. So cost = $85\times4=\$340$.

Step4: Calculate profit/loss

Profit (or loss) = Revenue - Cost = $204 - 340=-\$136$. A negative value means a loss.

Answer:

The booth will lose $\$136$.