Question

examine the worked example. then, answer each question.
christopher plays quarterback for a neighborhood football team. during his team’s first game, he executed 60 plays, 42 of which were successful. what percent of christopher’s plays were successful?
write a proportion to represent the problem. let ( p ) represent the percentage of christopher’s plays that were successful.
( \frac{square \text{ plays that were successful}}{square \text{ total plays}} = \frac{square}{100} )
( 100(square) = (square)p )
( square = p )
during the first game, ( square ) % of christopher’s plays were successful.

Explanation:

Step1: Set up the proportion

The formula for percentage is \(\frac{\text{part}}{\text{whole}}=\frac{\text{percentage}}{100}\). Here, the part (plays that were successful) is \(42\), the whole (total plays) is \(60\), and the percentage is \(p\). So the proportion is \(\frac{42}{60}=\frac{p}{100}\).

Step2: Cross - multiply

Cross - multiplying gives \(100\times42 = 60\times p\).

Step3: Solve for \(p\)

First, calculate \(100\times42=4200\). Then, since \(4200 = 60p\), we can solve for \(p\) by dividing both sides by \(60\). So \(p=\frac{4200}{60}=70\).

Answer:

\(\frac{42}{60}=\frac{p}{100}\); \(100\times42 = 60\times p\); \(70 = p\); \(70\)