Percent Proportion

Show your work for each problem.

1.
Which proportion matches the question "What percent of 50 is 20?"
1. a) $\frac{20}{100} = \frac{p}{50}$
2. b) $\frac{20}{50} = \frac{p}{100}$
3. c) $\frac{50}{20} = \frac{p}{100}$
4. d) $\frac{p}{20} = \frac{50}{100}$
Answer: $\frac{20}{50} = \frac{p}{100}$
The whole is 50 (after "of") and the part is 20, so $\frac{20}{50} = \frac{p}{100}$ . Solving gives $p = 40$ .
2.
What percent of 20 is 5? Enter the number without the % sign.
Answer: 25
$\frac{5}{20} = \frac{p}{100}$ gives $20p = 500$ , so $p = 25$ . 5 is $25\%$ of 20.
3.
Use the proportion $\frac{x}{85} = \frac{40}{100}$ to find 40% of 85.
Answer: 34
$100x = 3400$ , so $x = 34$ . 40% of 85 is 34.
4.
In "18 is 60% of what number?", which number is the part?
1. a)60
2. b)100
3. c)18
4. d)1080
Answer: 18
18 is the part, 60 is the percent and the whole is missing: $\frac{18}{x} = \frac{60}{100}$ , so $x = 30$ .
5.
What percent of 80 is 20?
Answer: 25
1. Which number is the whole (after "of")? 80
2. Cross multiply: what is $20 \times 100$ ? 2000
3. Divide 2000 by 80. What is $p$ ? 25
6.
9 is 30% of what number?
Answer: 30
1. Which number is the part? 9
2. Cross multiply: what is $9 \times 100$ ? 900
3. Divide 900 by 30. What is the whole? 30
7.
24 is 40% of what number?
Answer: 60
$40x = 2400$ , so $x = 60$ . Check: $40\%$ of 60 is $0.4 \times 60 = 24$ .
8.
Ana scored 27 out of 36 points on a test. What percent is that?
1. a)70%
2. b)75%
3. c)72%
4. d)60%
Answer: 75%
$36p = 2700$ , so $p = 75$ . Ana scored $75\%$ .
9.
Tom answered 42 of 50 questions correctly. What percent did he get right?
Answer: 84
1. What is the whole (all questions)? 50
2. Cross multiply: what is $42 \times 100$ ? 4200
3. Divide 4200 by 50. What is $p$ ? 84
10.
In a survey, 63 students chose pizza as their favorite lunch. That is 35% of the students surveyed. How many students were surveyed?
Answer: 180
1. Which number is the part? 63
2. Cross multiply: what is $63 \times 100$ ? 6300
3. Divide 6300 by 35. How many students were surveyed? 180
11.
Use the percent proportion to find 15% of 260.
Answer: 39
1. Which number is the whole? 260
2. Cross multiply: what is $15 \times 260$ ? 3900
3. Divide 3900 by 100. What is the part? 39
12.
63 is what percent of 90? Enter the number without the % sign.
Answer: 70
$90p = 6300$ , so $p = 70$ . 63 is $70\%$ of 90.
13.
Which equation do you get when you cross multiply $\frac{15}{x} = \frac{30}{100}$ ?
1. a) $15x = 3000$
2. b) $100x = 450$
3. c) $45x = 100$
4. d) $30x = 1500$
Answer: $30x = 1500$
On the diagonals: $15 \times 100 = 30 \times x$ , so $30x = 1500$ and $x = 50$ .
14.
A pair of shoes is 24% off and you save 18 dollars. What was the original price, and what do you pay? Give the price you pay in dollars.
Answer: 57
1. Cross multiply: what is $18 \times 100$ ? 1800
2. Divide 1800 by 24. What was the original price? 75
3. Subtract the savings. What do you pay? 57
15.
In a grade, 12 students walk to school. That is 15% of all students in the grade. How many students in the grade do NOT walk to school?
Answer: 68
1. Cross multiply: what is $12 \times 100$ ? 1200
2. Divide 1200 by 15. How many students are in the grade? 80
3. How many do NOT walk? 68
16.
In a poll of 120 people, 54 said they prefer tea to coffee. What percent prefer tea?
1. a)40%
2. b)45%
3. c)42%
4. d)54%
Answer: 45%
$120p = 5400$ , so $p = 45$ . $45\%$ prefer tea. (54% would wrongly treat 54 as the percent.)
17.
2.4 is 8% of what number?
Answer: 30
$8x = 2.4 \times 100 = 240$ , so $x = 30$ . Check: $8\%$ of 30 is $0.08 \times 30 = 2.4$ .
18.
Ana scored 18 out of 24 on test A and 34 out of 40 on test B. Find both percents. What is the higher percent?
Answer: 85
1. Test A: solve $\frac{18}{24} = \frac{p}{100}$ . What is $p$ ? 75
2. Test B: solve $\frac{34}{40} = \frac{p}{100}$ . What is $p$ ? 85
3. Which percent is higher? Enter the number. 85