Question

directions: use the percent proportion to solve each problem. round to the nearest tenth or cent when necessary.

1. find 24% of 165.
2. what percent of 30 is 16.5?
3. 24.39 is 9% of what number?
4. 2\frac{3}{5} is what percent of 20?
5. what is 48.75% of 204?
6. 16% of what number is 14?
7. 52 is what percent of 156?
8. find 59.2% of 250.
9. the yankees won 90 of their 162 games last season. what percent of the games did they win?
10. a school survey says that 75%, or 294 of the 8th - graders, have a cell phone. how many 8th - graders are there?

Explanation:

Step1: Recall percent - proportion formula

The percent - proportion is $\frac{a}{b}=\frac{p}{100}$, where $a$ is the part, $b$ is the whole, and $p$ is the percentage.

1. Find 24% of 165

Step1: Substitute into the formula

Here, $p = 24$ and $b=165$, and we want to find $a$. Using the formula $\frac{a}{b}=\frac{p}{100}$, we have $a=\frac{p\times b}{100}$.
$a=\frac{24\times165}{100}=\frac{3960}{100}=39.6$

2. What percent of 30 is 16.5?

Step1: Substitute into the formula

Let $p$ be the unknown percentage, $a = 16.5$ and $b = 30$. Then $\frac{16.5}{30}=\frac{p}{100}$.

Step2: Solve for $p$

Cross - multiply: $30p=16.5\times100 = 1650$. Then $p=\frac{1650}{30}=55$

3. 24.39 is 9% of what number?

Step1: Substitute into the formula

Let $b$ be the unknown number, $a = 24.39$ and $p = 9$. Then $\frac{24.39}{b}=\frac{9}{100}$.

Step2: Solve for $b$

Cross - multiply: $9b=24.39\times100 = 2439$. Then $b=\frac{2439}{9}=271$

4. $2\frac{3}{5}$ is what percent of 20?

Step1: Convert the mixed number to a decimal

$2\frac{3}{5}=2 + 0.6=2.6$. Let $p$ be the unknown percentage, $a = 2.6$ and $b = 20$. Then $\frac{2.6}{20}=\frac{p}{100}$.

Step2: Solve for $p$

Cross - multiply: $20p=2.6\times100 = 260$. Then $p=\frac{260}{20}=13$

5. What is 48.75% of 204?

Step1: Substitute into the formula

Here, $p = 48.75$ and $b = 204$, and we want to find $a$. Using the formula $a=\frac{p\times b}{100}$.
$a=\frac{48.75\times204}{100}=\frac{48.75\times204}{100}=\frac{9945}{100}=99.45$

6. 16% of what number is 14?

Step1: Substitute into the formula

Let $b$ be the unknown number, $a = 14$ and $p = 16$. Then $\frac{14}{b}=\frac{16}{100}$.

Step2: Solve for $b$

Cross - multiply: $16b=14\times100 = 1400$. Then $b=\frac{1400}{16}=87.5$

7. 52 is what percent of 156?

Step1: Substitute into the formula

Let $p$ be the unknown percentage, $a = 52$ and $b = 156$. Then $\frac{52}{156}=\frac{p}{100}$.

Step2: Solve for $p$

Cross - multiply: $156p=52\times100 = 5200$. Then $p=\frac{5200}{156}\approx33.3$

8. Find 59.2% of 250

Step1: Substitute into the formula

Here, $p = 59.2$ and $b = 250$, and we want to find $a$. Using the formula $a=\frac{p\times b}{100}$.
$a=\frac{59.2\times250}{100}=\frac{14800}{100}=148$

9. The Yankees won 90 of their 162 games last season. What percent of the games did they win?

Step1: Substitute into the formula

Let $p$ be the unknown percentage, $a = 90$ and $b = 162$. Then $\frac{90}{162}=\frac{p}{100}$.

Step2: Solve for $p$

Cross - multiply: $162p=90\times100 = 9000$. Then $p=\frac{9000}{162}\approx55.6$

10. A school survey says that 75%, or 294 of the 8th graders, have a cell phone. How many 8th graders are there?

Step1: Substitute into the formula

Let $b$ be the unknown number, $a = 294$ and $p = 75$. Then $\frac{294}{b}=\frac{75}{100}$.

Step2: Solve for $b$

Cross - multiply: $75b=294\times100 = 29400$. Then $b=\frac{29400}{75}=392$

Answer:

1. 39.6
2. 55%
3. 271
4. 13%
5. 99.45
6. 87.5
7. 33.3%
8. 148
9. 55.6%
10. 392