Question

solve using the proportion formula. state the part, whole, and percent for each situation. substitute the values into the proportional formula equation and solve. state your final result in a complete sentence using the appropriate units.

1. a select soccer team had tryouts for the upcoming spring season. the team typically has 25% of the players in the tryout process come back for a second evaluation. if the team asked 17 players back for a second evaluation, how many players showed up for the first tryout?

part =
whole =
percent =
substitute and solve:

Explanation:

Step1: Identify part, whole, percent

The part (players back for second evaluation) is what we need to find? Wait, no—wait, the problem says "25% of the players in the tryout process come back for a second evaluation. If the team asked 17 players back for a second evaluation, how many players showed up for the first tryout?" Wait, no, let's re-express. Wait, the formula for percent proportion is \(\frac{\text{part}}{\text{whole}}=\frac{\text{percent}}{100}\). Let's define:

• part: players back for second evaluation = 17 (wait, no—wait, 25% is the percent of the whole (first tryout players) that are the part (second evaluation players). So:

part = 17 (players back for second evaluation)

percent = 25 (25% of the whole)

whole =? (players at first tryout, what we need to find? Wait, no—wait, the question is "how many players showed up for the first tryout?" So whole is the first tryout players, part is 17 (25% of whole is 17). So:

part = 17

percent = 25

whole =? (let's call it \(x\))

Step2: Set up the proportion

Using \(\frac{\text{part}}{\text{whole}}=\frac{\text{percent}}{100}\), substitute:

\(\frac{17}{x}=\frac{25}{100}\)

Step3: Solve for \(x\)

Cross-multiply: \(25x = 17 \times 100\)

\(25x = 1700\)

Divide both sides by 25: \(x=\frac{1700}{25}=68\)

Wait, but the problem's initial blanks: "part = __", "whole = ", "percent = __". Let's fill those first.

Part: 17 (players back for second evaluation)

Percent: 25 (25% of the whole)

Whole:? (players at first tryout, which we solve for)

Then substitute into \(\frac{\text{part}}{\text{whole}}=\frac{\text{percent}}{100}\):

\(\frac{17}{\text{whole}}=\frac{25}{100}\)

Solving: whole = \(\frac{17 \times 100}{25}=68\)

Answer:

part = 17 (players)
whole = 68 (players)
percent = 25 (%)

Substitute and solve: Using \(\frac{17}{\text{whole}}=\frac{25}{100}\), cross - multiply to get \(25\times\text{whole}=17\times100\), then \(\text{whole}=\frac{1700}{25} = 68\). So the number of players at the first tryout is 68.