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Translate and solve: 6.5% of what number is $1.56 ?

Solution

Identify the parts of the percent proportion. .
Restate as a proportion. .
Set up the proportion. Let n = number. .
Find the cross products and set them equal. .
Simplify. .
Divide both sides by 6.5 to isolate the variable. .
Simplify. .
Write a complete sentence that answers the question. 6.5% of $24 is $1.56.
Check if the answer is reasonable. Yes. 6.5% is a small amount and $1.56 is much less than $24.
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Translate and solve using proportions: 8.5% of what number is $3.23 ?

38

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Translate and solve using proportions: 7.25% of what number is $4.64 ?

64

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Translate and solve using proportions: What percent of 72 is 9 ?

Solution

Identify the parts of the percent proportion. .
Restate as a proportion. .
Set up the proportion. Let n = number. .
Find the cross products and set them equal. .
Simplify. .
Divide both sides by 72. .
Simplify. .
Write a complete sentence that answers the question. 12.5% of 72 is 9.
Check if the answer is reasonable. Yes. 9 is 1 8 of 72 and 1 8 is 12.5%.
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Translate and solve using proportions: What percent of 72 is 27 ?

37.5%

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Translate and solve using proportions: What percent of 92 is 23 ?

25%

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Access additional online resources

Key concepts

  • Use the Definition of Proportion. See [link] .
  • Solve Proportions. See [link] .
  • Solve Applications Using Proportions. See [link] .
  • Write Percent Equations as Proportions. See [link] .
  • Translate and Solve Percent Proportions. See [link] .

Practice makes perfect

Use the Definition of Proportion

In the following exercises, write each sentence as a proportion.

4 is to 15 as 36 is to 135 .

4 15 = 36 135

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7 is to 9 as 35 is to 45 .

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12 is to 5 as 96 is to 40 .

12 5 = 96 40

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15 is to 8 as 75 is to 40 .

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5 wins in 7 games is the same as 115 wins in 161 games.

5 7 = 115 161

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4 wins in 9 games is the same as 36 wins in 81 games.

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8 campers to 1 counselor is the same as 48 campers to 6 counselors.

8 1 = 48 6

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6 campers to 1 counselor is the same as 48 campers to 8 counselors.

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$9.36 for 18 ounces is the same as $2.60 for 5 ounces.

9.36 18 = 2.60 5

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$3.92 for 8 ounces is the same as $1.47 for 3 ounces.

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$18.04 for 11 pounds is the same as $4.92 for 3 pounds.

18.04 11 = 4.92 3

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$12.42 for 27 pounds is the same as $5.52 for 12 pounds.

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In the following exercises, determine whether each equation is a proportion.

13.5 8.5 = 31.05 19.55

yes

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Solve Proportions

In the following exercises, solve each proportion.

Solve Applications Using Proportions

In the following exercises, solve the proportion problem.

Pediatricians prescribe 5 milliliters (ml) of acetaminophen for every 25 pounds of a child’s weight. How many milliliters of acetaminophen will the doctor prescribe for Jocelyn, who weighs 45 pounds?

9 ml

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Brianna, who weighs 6 kg, just received her shots and needs a pain killer. The pain killer is prescribed for children at 15 milligrams (mg) for every 1 kilogram (kg) of the child’s weight. How many milligrams will the doctor prescribe?

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At the gym, Carol takes her pulse for 10 sec and counts 19 beats. How many beats per minute is this? Has Carol met her target heart rate of 140 beats per minute?

114, no

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Practice Key Terms 3

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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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