Question

directions: use the percent - proportion to solve each problem. 1. 18 is what percent of 40? 2. what percent of 75 is 10? 3. what is 30% of 15? 4. find 8.5% of 160. 5. 28 is 4% of what number? 6. 86% of what number is 77.4? 7. find 28.5% of 200. 8. 52 is what percent of 125? 9. 7.5% of what number is 21? 10. what is 64% of 80?

Explanation:

Step1: Recall percent - proportion formula

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

Problem 1: 18 is what percent of 40?

Let $a = 18$, $b = 40$, and $p$ be the unknown percentage.

Step1: Set up the proportion

$\frac{18}{40}=\frac{p}{100}$

Step2: Cross - multiply

$18\times100 = 40\times p$
$1800=40p$

Step3: Solve for $p$

$p=\frac{1800}{40}=45$

Problem 2: What percent of 75 is 30?

Let $a = 30$, $b = 75$, and $p$ be the unknown percentage.

Step1: Set up the proportion

$\frac{30}{75}=\frac{p}{100}$

Step2: Cross - multiply

$30\times100 = 75\times p$
$3000 = 75p$

Step3: Solve for $p$

$p=\frac{3000}{75}=40$

Problem 3: What is 30% of 15?

Let $p = 30$, $b = 15$, and $a$ be the unknown part.

Step1: Set up the proportion

$\frac{a}{15}=\frac{30}{100}$

Step2: Cross - multiply

$100a=15\times30$
$100a = 450$

Step3: Solve for $a$

$a=\frac{450}{100}=4.5$

Problem 4: Find 8.5% of 160

Let $p = 8.5$, $b = 160$, and $a$ be the unknown part.

Step1: Set up the proportion

$\frac{a}{160}=\frac{8.5}{100}$

Step2: Cross - multiply

$100a=160\times8.5$
$100a = 1360$

Step3: Solve for $a$

$a=\frac{1360}{100}=13.6$

Problem 5: 28 is 4% of what number?

Let $a = 28$, $p = 4$, and $b$ be the unknown whole.

Step1: Set up the proportion

$\frac{28}{b}=\frac{4}{100}$

Step2: Cross - multiply

$4b=28\times100$
$4b = 2800$

Step3: Solve for $b$

$b=\frac{2800}{4}=700$

Problem 6: 86% of what number is 77.4?

Let $a = 77.4$, $p = 86$, and $b$ be the unknown whole.

Step1: Set up the proportion

$\frac{77.4}{b}=\frac{86}{100}$

Step2: Cross - multiply

$86b=77.4\times100$
$86b = 7740$

Step3: Solve for $b$

$b=\frac{7740}{86}=90$

Problem 7: Find 28.5% of 200

Let $p = 28.5$, $b = 200$, and $a$ be the unknown part.

Step1: Set up the proportion

$\frac{a}{200}=\frac{28.5}{100}$

Step2: Cross - multiply

$100a=200\times28.5$
$100a = 5700$

Step3: Solve for $a$

$a=\frac{5700}{100}=57$

Problem 8: 32 is what percent of 125?

Let $a = 32$, $b = 125$, and $p$ be the unknown percentage.

Step1: Set up the proportion

$\frac{32}{125}=\frac{p}{100}$

Step2: Cross - multiply

$32\times100 = 125\times p$
$3200 = 125p$

Step3: Solve for $p$

$p=\frac{3200}{125}=25.6$

Problem 9: 7.5% of what number is 21?

Let $a = 21$, $p = 7.5$, and $b$ be the unknown whole.

Step1: Set up the proportion

$\frac{21}{b}=\frac{7.5}{100}$

Step2: Cross - multiply

$7.5b=21\times100$
$7.5b = 2100$

Step3: Solve for $b$

$b=\frac{2100}{7.5}=280$

Problem 10: What is 64% of 80?

Let $p = 64$, $b = 80$, and $a$ be the unknown part.

Step1: Set up the proportion

$\frac{a}{80}=\frac{64}{100}$

Step2: Cross - multiply

$100a=80\times64$
$100a = 5120$

Step3: Solve for $a$

$a=\frac{5120}{100}=51.2$

Answer:

1. 45%
2. 40%
3. 4.5
4. 13.6
5. 700
6. 90
7. 57
8. 25.6%
9. 280
10. 51.2