Mathematics » Mathematics 106: Percents » Solve Proportions and their Applications

How to Translate and Solve Percent Proportions

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How to Translate and Solve Percent Proportions

Now that we have written percent equations as proportions, we are ready to solve the equations.

Example

Translate and solve using proportions: What number is \(\text{45%}\) of \(80?\)

Solution

Identify the parts of the percent proportion.How to Translate and Solve Percent Proportions
Restate as a proportion.How to Translate and Solve Percent Proportions
Set up the proportion. Let \(n=\) number.How to Translate and Solve Percent Proportions
Find the cross products and set them equal.How to Translate and Solve Percent Proportions
Simplify.How to Translate and Solve Percent Proportions
Divide both sides by 100.How to Translate and Solve Percent Proportions
Simplify.How to Translate and Solve Percent Proportions
Check if the answer is reasonable. 
Yes. 45 is a little less than half of 100 and 36 is a little less than half 80. 
Write a complete sentence that answers the question.36 is 45% of 80.

In the next example, the percent is more than \(100,\) which is more than one whole. So the unknown number will be more than the base.

Example

Translate and solve using proportions: \(\text{125%}\) of \(25\) is what number?

Solution

Identify the parts of the percent proportion.How to Translate and Solve Percent Proportions
Restate as a proportion.How to Translate and Solve Percent Proportions
Set up the proportion. Let \(n=\) number.How to Translate and Solve Percent Proportions
Find the cross products and set them equal.How to Translate and Solve Percent Proportions
Simplify.How to Translate and Solve Percent Proportions
Divide both sides by 100.How to Translate and Solve Percent Proportions
Simplify.How to Translate and Solve Percent Proportions
Check if the answer is reasonable. 
Yes. 125 is more than 100 and 31.25 is more than 25. 
Write a complete sentence that answers the question.125% of 25 is 31.25.

Percents with decimals and money are also used in proportions.

Example

Translate and solve: \(\text{6.5%}\) of what number is \(\text{\$1.56}?\)

Solution

Identify the parts of the percent proportion.How to Translate and Solve Percent Proportions
Restate as a proportion.How to Translate and Solve Percent Proportions
Set up the proportion. Let\(n=\) number.How to Translate and Solve Percent Proportions
Find the cross products and set them equal.How to Translate and Solve Percent Proportions
Simplify.How to Translate and Solve Percent Proportions
Divide both sides by 6.5 to isolate the variable.How to Translate and Solve Percent Proportions
Simplify.How to Translate and Solve Percent Proportions
Check if the answer is reasonable. 
Yes. 6.5% is a small amount and \$1.56 is much less than \$24. 
Write a complete sentence that answers the question.6.5% of \$24 is \$1.56.

Example

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

Solution

Identify the parts of the percent proportion.How to Translate and Solve Percent Proportions
Restate as a proportion.How to Translate and Solve Percent Proportions
Set up the proportion. Let \(n=\) number.How to Translate and Solve Percent Proportions
Find the cross products and set them equal.How to Translate and Solve Percent Proportions
Simplify.How to Translate and Solve Percent Proportions
Divide both sides by 72.How to Translate and Solve Percent Proportions
Simplify.How to Translate and Solve Percent Proportions
Check if the answer is reasonable. 
Yes. 9 is \(\frac{1}{8}\) of 72 and \(\frac{1}{8}\) is 12.5%. 
Write a complete sentence that answers the question.12.5% of 72 is 9.

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