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Percent Equation to Find Part a

Find x% of a number

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Use the Percent Equation to Find Part a

Let’s Think About It

Credit: Will Clayton
Source: https://www.flickr.com/photos/spool32/5045502202/in/photolist-8FRw2h-a61vNH-kAyzMV-rXnbt-6h1NjG-pyU2f-eeq4k-o43p9g-8Xhvjh-Fj8W5-foNHkM-7fziqU-bZFXeh-cBvFFY-3J7mXR-kWhWuN-6kHUV2-8GVHpA-anBR52-6bHtCa-7cFeaz-6wuEnF-7Fn74k-of9yaQ-7cK8eG-6NvoXd-pgp5rz-fErH-6BDPGJ-7iuvNx-5CSvo6-6f4b1Z-9MntAh-2EKn3V-5mFytx-6Z3tfB-9Z1hGR-pL494B-bmhQ9h-bp9m9-4wEJLc-4wheVs-dTyha1-5YKRDj-8K1F5u-4wttVC-eiBg7T-eeq5b-fyL2gf-5Z6dkC
License: CC BY-NC 3.0

Jordan received $85 from his aunts for his birthday. He wants to buy a new game for his computer. His mother told him he could spend no more than 28% of his money on a computer game. How much money can Jordan spend?

In this concept, you will learn to use the percent equation to find part a.

Guidance

You can use the proportion ab=p100 to solve for a percent. You can also solve percent problems by using an equation. In this concept, you will use a proportion to create a different kind of equation that will help you solve percent problems. 

When you solve the proportion ab=p100, you cross multiply to find the missing variable. You can rearrange this formula so that you are solving for just the variable a.

ab100a100a100a====p100pbpb100pb100
You could also say that a=pb100 is equal to a=0.01pb. As well, you could convert your percent directly into a decimal and therefore the formula becomes even simpler.

Let’s look at an example.

What is 85% of 90?

First, change the 85% into a decimal. You know that percent means that the denominator of the fraction is 100.

Therefore, 85%=0.85.

Next, multiply using the percent equation.

aaa===0.01pb0.85×9076.5
The answer is 76.5.

Let’s look at another example.

What is 7% of 900?

First, change the 7% into a decimal. You know that percent means that the denominator of the fraction is 100.

Therefore, 7%=0.07.

Next, multiply using the percent equation.

aaa===0.01pb0.07×90063
The answer is 63.

Guided Practice

What is 19% of 300?

First, change the 19% into a decimal.

19%=0.19

Next, multiply using the percent equation.

aaa===0.01pb0.19×30057
The answer is 57.

Examples

Example 1

What is 22% of 100?

First, change the 22% into a decimal.

22%=0.22

Next, multiply using the percent equation.

aaa===0.01pb0.22×10022
 

The answer is 22.

Example 2

What is 8% of 57?

First, change the 8% into a decimal.

8%=0.08

Next, multiply using the percent equation.

aaa===0.01pb0.08×574.56

The answer is 4.56.

Example 3

What is 17% of 80?

First, change the 17% into a decimal.

17%=0.17

Next, multiply using the percent equation.

aaa===0.01pb0.17×8013.6
The answer is 13.6.

Follow Up

Credit: @sage_solar
Source: https://www.flickr.com/photos/sagesolar/17050225387/in/photolist-rYERZe-bUf8df-4C7Vjn-6XMQds-9Zq8aQ-fgvs15-4Cjm8N-cw2W5N-8XPvG9-dL6sts-b2Y1vX-5Ukkoh-8XPvNf-627f6c-tFuRZ-5yk9cA-4s5faN-66GAT5-zWvFc-8XLsAg-8XPvWE-fhQF2E-7uHYQc-74SikE-9YB5BL-6Y1Rbx-77rfcL-bmJtgf-dgL9Mi-76gq1m-4LZpGt-8XPvUj-2t6pUU-8XMQzX-nwbo4z-9xBJ67-4CeU4J-6AX6MS-omAqpT-69W4Z4-8H1Ar6-31JdM-5ydj3i-9JfDUW-556MQr-6LNmy5-bXqpLL-5yk97L-h6VmX-dczXg5
License: CC BY-NC 3.0

Remember Jordan and his partial spending money?

Jordan has $85 from his birthday but cannot spend any more than 28% of it on his new computer game. How much can he spend?

First, change the 28% into a decimal.

28%=0.28

Next, multiply using the percent equation.

aaa===0.01pb0.28×8523.8
The answer is 23.8.

Therefore, Jordan can spend up to $23.80 on his new computer game.

Video Review

https://www.youtube.com/watch?v=LkTYkHbUiU4

Explore More

Solve each percent problem. Round your answers to the nearest tenth when necessary.

  1. How much is 15% of 73?
  2. What is 70% of 5?
  3. What is 3% of 4 million?
  4. What is 18% of 30?
  5. What is 22% of 56?
  6. What is 19% of 300?
  7. What is 21% of 45?
  8. What is 34% of 250?
  9. What is 33% of 675?
  10. What is 3% of 700?
  11. What is 11% of 955?
  12. What is 14% of 55?
  13. What is 37% of 17?
  14. What is 20% of 9?
  15. What is 2% of 18?


Vocabulary

Decimal

Decimal

In common use, a decimal refers to part of a whole number. The numbers to the left of a decimal point represent whole numbers, and each number to the right of a decimal point represents a fractional part of a power of one-tenth. For instance: The decimal value 1.24 indicates 1 whole unit, 2 tenths, and 4 hundredths (commonly described as 24 hundredths).
Inverse Operation

Inverse Operation

Inverse operations are operations that "undo" each other. Multiplication is the inverse operation of division. Addition is the inverse operation of subtraction.
Proportion

Proportion

A proportion is an equation that shows two equivalent ratios.

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