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Five years ago a woman had an annual income of $19,200. She presently earns $42,000 annually. By what percent has her salary increased? Round the result to two decimal places.

We need to determine the percent.

42,000 is what percent of 19,200 ? Missing factor statement. (percentage) = (percent) (base) 42,000 = Q 19,200

Q = 42,000 ÷ 19,200 Divide. Q = 2.1875 Round to two decimal places. Q = 2.19 Convert to a percent. Q = 219% Convert to a percent.

Thus, this woman's annual salary has increased 219%.

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Practice set b

99.13 is what percent of 431?

23%

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On an 80 question exam, a student got 72 correct answers. What percent did the student get on the exam?

90%

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A bottle contains 45 milliliters of sugar and 67 milliliters of water. What fraction of sugar does the bottle contain? Round the result to two decimal places (then express as a percent).

40%

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Finding the base

Sample set c

15 is 30 % of what number? Missing factor statement. (percentage) = (percent) (base) [(percentage) = (factor) ⋅ (factor)] 15 = 30 % B Convert to decimals. 15 = .30 B [(missing factor) = (product) ÷ (known factor)]

B = 15 ÷ .30 B = 50

Thus, 15 is 30% of 50.

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56.43 is 33 % of what number? Missing factor statement. (percentage) = (percent) (base) 56.43 = 33 % B Convert to decimals. 56.43 = .33 B Divide.

B = 56.43 ÷ .33 B = 171

Thus, 56.43 is 33% of 171.

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Fifteen milliliters of water represents 2% of a hydrochloric acid (HCl) solution. How many milliliters of solution are there?

We need to determine the total supply. The word supply indicates base .

15 is 2 % of what number? Missing factor statement. (percentage) = (percent) (base) 15 = 2 % B Convert to decimals. 15 = .02 B Divide.

B = 15 ÷ .02 B = 750

Thus, there are 750 milliliters of solution in the bottle.

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In a particular city, a sales tax of 6 1 2 size 12{6 { {1} over {2} } } {} % is charged on items purchased in local stores. If the tax on an item is $2.99, what is the price of the item?

We need to determine the price of the item. We can think of price as the starting place . Starting place indicates base . We need to determine the base.

2.99 is 6 1 2 % of what number? Missing factor statement. (percentage) = (percent) (base) 2.99 = 6 1 2 % B Convert to decimals. 2.99 = 6.5 % B 2.99 = .065 B [(missing factor) = (product) ÷ (known factor)]

B = 2.99 ÷ .065 Divide. B = 46

Thus, the price of the item is $46.00.

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A clothing item is priced at $20.40. This marked price includes a 15% discount. What is the original price?

We need to determine the original price. We can think of the original price as the starting place . Starting place indicates base . We need to determine the base. The new price, $20.40, represents 100% - 15% = 85% size 12{"100% - 15% "=" 85%"} {} of the original price.

20.40 is 85 % of what number? Missing factor statement. (percentage) = (percent) (base) 20.40 = 85 % B Convert to decimals. 20.40 = .85 B [(missing factor) = (product) ÷ (known factor)]

B = 20.40 ÷ .85 Divide. B = 24

Thus, the original price of the item is $24.00.

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Practice set c

1.98 is 2% of what number?

99

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3.3 milliliters of HCl represents 25% of an HCl solution. How many milliliters of solution are there?

13.2ml

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A salesman, who makes a commission of 18 1 4 size 12{"18" { {1} over {4} } } {} % on each sale, makes a commission of $152.39 on a particular sale. Rounded to the nearest dollar, what is the amount of the sale?

$835

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Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
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