Question

write and solve a proportion to answer the question.

1. what percent of 25 is 12?
2. 14 is what percent of 56?
3. 25% of what number is 9?
4. 36 is 0.9% of what number?
5. 75% of 124 is what number?
6. 110% of 90 is what number
7. what number is 0.4% of 40?
8. 72 is what percent of 45?

Explanation:

Step1: Solve Question 11

Let \( x \) be the percentage. The proportion is \( \frac{x}{100}=\frac{12}{25} \). Cross - multiply: \( 25x = 12\times100 \), so \( 25x=1200 \), then \( x=\frac{1200}{25} = 48 \).

Step2: Solve Question 12

Let \( y \) be the percentage. The proportion is \( \frac{y}{100}=\frac{14}{56} \). Cross - multiply: \( 56y = 14\times100 \), so \( 56y = 1400 \), then \( y=\frac{1400}{56}=25 \).

Step3: Solve Question 13

Let \( z \) be the number. The proportion is \( \frac{25}{100}=\frac{9}{z} \). Cross - multiply: \( 25z=9\times100 \), so \( 25z = 900 \), then \( z=\frac{900}{25}=36 \).

Step4: Solve Question 14

Let \( w \) be the number. The proportion is \( \frac{0.9}{100}=\frac{36}{w} \). Cross - multiply: \( 0.9w=36\times100 \), so \( 0.9w = 3600 \), then \( w=\frac{3600}{0.9}=4000 \).

Step5: Solve Question 15

Let \( m \) be the number. The proportion is \( \frac{75}{100}=\frac{124}{m} \). Cross - multiply: \( 75m = 124\times100 \), so \( 75m=12400 \), then \( m=\frac{12400}{75}=\frac{496}{3}\approx165.33 \).

Step6: Solve Question 16

Let \( n \) be the number. The proportion is \( \frac{110}{100}=\frac{110\%\text{ of }90}{n}=\frac{99}{n} \). Cross - multiply: \( 110n=99\times100 \), so \( 110n = 9900 \), then \( n=\frac{9900}{110}=90 \).

Step7: Solve Question 17

Let \( p \) be the number. The proportion is \( \frac{0.4}{100}=\frac{p}{40} \). Cross - multiply: \( 100p=0.4\times40 \), so \( 100p = 16 \), then \( p=\frac{16}{100}=0.16 \).

Step8: Solve Question 18

Let \( q \) be the percentage. The proportion is \( \frac{q}{100}=\frac{72}{45} \). Cross - multiply: \( 45q=72\times100 \), so \( 45q = 7200 \), then \( q=\frac{7200}{45}=160 \).

Answer:

1. \( 48\% \)
2. \( 25\% \)
3. \( 36 \)
4. \( 4000 \)
5. \( \frac{496}{3}\approx165.33 \)
6. \( 90 \)
7. \( 0.16 \)
8. \( 160\% \)