Writing and Solving Percent Proportions
Learning Outcomes
- Translate a statement to a proportion
- Solve a percent proportion
Previously, we solved percent equations by applying the properties of equality we have used to solve equations throughout this text. Some people prefer to solve percent equations by using the proportion method. The proportion method for solving percent problems involves a percent proportion. A percent proportion is an equation where a percent is equal to an equivalent ratio.
For example, \text{60%}=\frac{60}{100} and we can simplify 10060=53. Since the equation 10060=53 shows a percent equal to an equivalent ratio, we call it a percent proportion. Using the vocabulary we used earlier:
baseamount=100percent
53=10060
Percent Proportion
The amount is to the base as the percent is to
100.
baseamount=100percent
If we restate the problem in the words of a proportion, it may be easier to set up the proportion:
The amount is to the base as the percent is to one hundred.
We could also say:
The amount out of the base is the same as the percent out of one hundred.
First we will practice translating into a percent proportion. Later, we’ll solve the proportion.
example
Translate to a proportion. What number is
\text{75%} of
90?
Solution
If you look for the word "of", it may help you identify the base.
Identify the parts of the percent proportion. |
 |
Restate as a proportion. |
What number out of 90 is the same as 75 out of 100? |
Set up the proportion. Let n=number . |
90n=10075 |
try it
[ohm_question]146821[/ohm_question]
example
Translate to a proportion.
19 is
\text{25%} of what number?
Answer:
Solution
Identify the parts of the percent proportion. |
 |
Restate as a proportion. |
19 out of what number is the same as 25 out of 100? |
Set up the proportion. Let n=number . |
n19=10025 |
try it
[ohm_question]146822[/ohm_question]
example
Translate to a proportion. What percent of
27 is
9?
Answer:
Solution
Identify the parts of the percent proportion. |
 |
Restate as a proportion. |
9 out of 27 is the same as what number out of 100? |
Set up the proportion. Let p=percent . |
279=100p |
try it
[ohm_question]146825[/ohm_question]
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?
Answer:
Solution
Identify the parts of the percent proportion. |
 |
Restate as a proportion. |
What number out of 80 is the same as 45 out of 100? |
Set up the proportion. Let n= number. |
80n=10045 |
Find the cross products and set them equal. |
100⋅n=80⋅45 |
Simplify. |
100n=3,600 |
Divide both sides by 100. |
100100n=1003,600 |
Simplify. |
n=36 |
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\text{%} of 80. |
try it
[ohm_question]146828[/ohm_question]
The following video shows a similar example of how to solve a percent proportion.
https://youtu.be/cApv0GeF2XM
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?
Answer:
Solution
Identify the parts of the percent proportion. |
 |
Restate as a proportion. |
What number out of 25 is the same as 125 out of 100? |
Set up the proportion. Let n= number. |
25n=100125 |
Find the cross products and set them equal. |
100⋅n=25⋅125 |
Simplify. |
100n=3,125 |
Divide both sides by 100. |
100100n=1003,125 |
Simplify. |
n=31.25 |
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\text{%} of 25 is 31.25. |
try it
[ohm_question]146839[/ohm_question]
Percents with decimals and money are also used in proportions.
example
Translate and solve:
\text{6.5%} of what number is
$1.56?
Answer:
Solution
Identify the parts of the percent proportion. |
 |
Restate as a proportion. |
$1.56 out of what number is the same as 6.5 out of 100? |
Set up the proportion. Let n= number. |
n1.56=1006.5 |
Find the cross products and set them equal. |
100⋅1.56=n⋅6.5 |
Simplify. |
156=6.5n |
Divide both sides by 6.5 to isolate the variable. |
6.5156=6.56.5n |
Simplify. |
24=n |
Check if the answer is reasonable. |
|
Yes. 6.5\text{%} is a small amount and $1.56 is much less than $24. |
|
Write a complete sentence that answers the question. |
6.5\text{%} of $24 is $1.56. |
try it
[ohm_question]146840[/ohm_question]
In the following video we show a similar problem, note the different wording that results in the same equation.
https://youtu.be/wsBhmrmumJo
example
Translate and solve using proportions: What percent of
72 is
9?
Answer:
Solution
Identify the parts of the percent proportion. |
 |
Restate as a proportion. |
9 out of 72 is the same as what number out of 100? |
Set up the proportion. Let n= number. |
729=100n |
Find the cross products and set them equal. |
72⋅n=100⋅9 |
Simplify. |
72n=900 |
Divide both sides by 72. |
7272n=72900 |
Simplify. |
n=12.5 |
Check if the answer is reasonable. |
|
Yes. 9 is 81 of 72 and 81 is 12.5\text{%}. |
|
Write a complete sentence that answers the question. |
12.5\text{%} of 72 is 9. |
try it
[ohm_question]146843[/ohm_question]
Watch the following video to see a similar problem.
https://youtu.be/1GTPRROi1tELicenses & Attributions
CC licensed content, Original
- Question ID 146843, 146840, 146839, 146828. Authored by: Lumen Learning. License: CC BY: Attribution.
CC licensed content, Shared previously
- Example 2: Solve a Percent Problem Using a Percent Proportion. Authored by: James Sousa (Mathispower4u.com). License: CC BY: Attribution.
- Example 3: Determine What Percent One Number is of Another Using a Percent Proportion. Authored by: James Sousa (Mathispower4u.com). License: CC BY: Attribution.
CC licensed content, Specific attribution
- Prealgebra. Provided by: OpenStax License: CC BY: Attribution. License terms: Download for free at http://cnx.org/contents/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757.