Percent Equation

Show your work for each problem.

1.
Which equation matches the question "What number is 40% of 65?"
1. a) $65x = 0.40$
2. b) $0.40x = 65$
3. c) $x = 40 \times 65$
4. d) $x = 0.40 \times 65$
Answer: $x = 0.40 \times 65$
Word by word: $x = 0.40 \times 65$ . The rate must be the decimal 0.40, not 40. The answer is $x = 26$ .
2.
In a percent sentence such as "20% of 50", which operation does the word "of" stand for?
1. a)Addition (+)
2. b)Multiplication (×)
3. c)Subtraction (-)
4. d)Division (÷)
Answer: Multiplication (×)
"Of" means multiplication: 20% of 50 is $0.2 \times 50 = 10$ . The word "is" stands for the equal sign.
3.
Which equation solves "12 is 30% of what number?"
1. a) $x = 0.30 \times 12$
2. b) $12 = 30x$
3. c) $0.30 = 12x$
4. d) $12 = 0.30x$
Answer: $12 = 0.30x$
"12 is" gives $12 =$ and "30% of what number" gives $0.30x$ , so $12 = 0.30x$ and $x = 12 \div 0.30 = 40$ .
4.
Which decimal is equal to 0.6%?
1. a)0.6
2. b)0.06
3. c)0.006
4. d)0.0006
Answer: 0.006
$0.6\% = 0.6 \div 100 = 0.006$ . Check: 0.6% of 1000 is $0.006 \times 1000 = 6$ .
5.
Without calculating exactly: how does 175% of 40 compare with 40?
1. a)It is less than 40
2. b)It is equal to 40
3. c)It is greater than 40
4. d)It is less than half of 40
Answer: It is greater than 40
A rate above 100% is a decimal greater than 1 ( $175\% = 1.75$ ), so the part is bigger than the whole: $1.75 \times 40 = 70 > 40$ .
6.
What number is 35% of 60?
Answer: 21
$x = 0.35 \times 60 = 21$ , so 21 is 35% of 60.
7.
24 is 50% of what number?
Answer: 48
$24 = 0.5x$ , so $x = 24 \div 0.5 = 48$ . Check: half of 48 is 24.
8.
27 is what percent of 90? Write only the number, without the % sign.
Answer: 30
$27 = r \times 90$ , so $r = 27 \div 90 = 0.3$ and $0.3 \times 100 = 30$ . 27 is 30% of 90.
9.
0.5% of what number is 3?
Answer: 600
$0.005x = 3$ , so $x = 3 \div 0.005 = 600$ . Check: $0.005 \times 600 = 3$ .
10.
63 is what percent of 45? Write only the number, without the % sign.
Answer: 140
$63 = r \times 45$ , so $r = 63 \div 45 = 1.4$ and $1.4 \times 100 = 140$ . 63 is 140% of 45.
11.
What is 15% of 220?
Answer: 33
1. Write 15% as a decimal. 0.15
2. Calculate $0.15 \times 220$ . 33
12.
9 is 20% of what number?
Answer: 45
1. Write 20% as a decimal. 0.2
2. The equation is $9 = 0.2x$ . Divide 9 by 0.2. What is $x$ ? 45
13.
21 is what percent of 60?
Answer: 35
1. Which number is the whole? 60
2. Calculate the rate $r = 21 \div 60$ as a decimal. 0.35
3. Multiply by 100. What percent is it? Write only the number. 35
14.
A jacket costs 72 dollars this year. That is 120% of last year's price. What was last year's price in dollars?
Answer: 60
1. Write 120% as a decimal. 1.2
2. Solve $72 = 1.2x$ . What is $x$ ? 60
15.
Nora answered 46 of 50 questions correctly. What percent of the questions did she get right? Write only the number.
Answer: 92
1. Calculate the rate $r = 46 \div 50$ as a decimal. 0.92
2. Multiply by 100. What percent is it? 92
16.
0.25% of what number is 7?
Answer: 2800
1. Write 0.25% as a decimal. 0.0025
2. Solve $0.0025x = 7$ . What is $x$ ? 2800
3. Check: what is $0.0025 \times 2800$ ? 7
17.
4.5 is what percent of 600? Write only the number.
Answer: 0.75
1. Calculate the rate $r = 4.5 \div 600$ as a decimal. 0.0075
2. Multiply by 100. What percent is it? 0.75
18.
38 is 95% of what number? Solve it with the percent equation, then check it with the proportion $\frac{38}{x} = \frac{95}{100}$ .
Answer: 40
1. Write 95% as a decimal. 0.95
2. Solve $38 = 0.95x$ . What is $x$ ? 40
3. Proportion check, first cross product: what is $38 \times 100$ ? 3800
4. Second cross product with $x = 40$ : what is $95 \times 40$ ? 3800