Question

question 1 (multiple choice worth 2 points) the swimming team has competed in 45 races this season. they have won 30 races so far. how many races will the team need to win today for the team to have a 75% success rate? 8 10 12 15

Explanation:

Step1: Define variables

Let \( x = \) races to win today. Total races become \( 45 + x \), total wins become \( 30 + x \).

Step2: Set up success rate equation

Success rate = \( \frac{\text{total wins}}{\text{total races}} = 0.75 \), so \( \frac{30 + x}{45 + x} = 0.75 \).

Step3: Solve for x

Multiply both sides by \( 45 + x \): \( 30 + x = 0.75(45 + x) \).
Expand right side: \( 30 + x = 33.75 + 0.75x \).
Subtract \( 0.75x \) and 30: \( 0.25x = 3.75 \).
Divide by 0.25: \( x = 15 \).

Answer:

15