# 1.9: Solving Problems Using Percents

- Page ID
- 45768

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### Learning Outcome

- Evaluate expressions and word problems involving percents

In this section we will solve percent questions by identifying the parts of the problem. We’ll look at a common application of percent—tips to a server at a restaurant—to see how to set up a basic percent application.

When Aolani and her friends ate dinner at a restaurant, the bill came to . They wanted to leave a tip. What amount would the tip be?

To solve this, we want to find what *amount* is of . The is called the *base*. The *percent* is the given . The amount of the tip would be , or — see the image below. To find the amount of the tip, we multiplied the percent by the base.

A tip for an restaurant bill comes out to .

### Pieces of a Percent Problem

Percent problems involve three quantities: the * base* amount (the whole), the

*, and the*

**percent***(a part of the whole or partial amount).*

**amount**The amount is a percent of the base.

Let’s look at another example:

Jeff has a Guitar Strings coupon for off any purchase of or more. He wants to buy a used guitar that has a price tag of on it. Jeff wonders how much money the coupon will take off the original price. Problems involving percents will have some combination of these three quantities to work with: the *percent*, the *amount*, and the *base*. The percent has the percent symbol (%) or the word percent. In the problem above, is the percent off the purchase price. The base is the whole amount or original amount. In the problem above, the “whole” price of the guitar is , which is the base. The amount is the unknown and what we will need to calculate.

There are thee cases: a missing amount, a missing percent or a missing base. Let’s take a look at each possibility.

## Solving for the Amount

When solving for the amount in a percent problem, you will multiply the percent (as a decimal or fraction) by the base. Typically we choose the decimal value for percent.

### Example

Find of

Solution:

First identify each piece of the problem:

percent: or

base:

amount: unknown

Now plug them into your equation

Therefore, is the amount or part that is of .

### Example

What is of ?

[reveal-answer q=”813233″]Show Answer[/reveal-answer]

[hidden-answer a=”813233″]

The base is and the percent is , so amount

[/hidden-answer]

### Try It

[ohm_question]80094[/ohm_question]

## Solving for the Percent

When solving for the percent in a percent problem, you will divide the amount by the base. The equation above is rearranged and the percent will come back as a decimal of fraction you can report in the form asked of you.

### Example

What percent of is ?

Solution:

First identify each piece of the problem:

percent: unknown

base:

amount:

Now plug the values into your equation

Therefore, is of .

### TRY IT

[ohm_question]80097[/ohm_question]

## Solving for the Base

When solving for the base in a percent problem, you will divide the amount by the percent (as a decimal or fraction). The equation above is rearranged and you will find the base after plugging in the values.

### EXample

is of what number?

Solution:

First identify each piece of the problem:

percent: or

base: unknown

amount:

Now plug the values into your equation

Therefore, is of .

### Example

An article says that of a non-profit’s donations, about a year, comes from individual donors. What is the total amount of donations the non-profit receives?

[reveal-answer q=”731314″]Show Answer[/reveal-answer]

[hidden-answer a=”731314″]

The percent is , and is the amount (or part of the whole). We are looking for the base.

*base* =

The non-profit receives a year in donations

[/hidden-answer]

### TRY IT

[ohm_question]157022[/ohm_question]

Here are a few more percent problems for you to try.

### try it

[ohm_question]146672[/ohm_question]

### try it

[ohm_question]146692[/ohm_question]

### try it

[ohm_question]146693[/ohm_question]

Many applications of percent occur in our daily lives, such as tips, sales tax, discount, and interest. To solve these applications we’ll translate to a basic percent equation, just like those we solved in the previous examples in this section. Once you translate the sentence into a percent equation, you know how to solve it.

### example

Dezohn and his girlfriend enjoyed a dinner at a restaurant, and the bill was . They want to leave an tip. If the tip will be of the total bill, how much should the tip be?

Solution

What are you asked to find? | the amount of the tip |

What formula/equation should you use? | |

Substitute in the correct values. | |

Solve. | |

Write a complete sentence that answers the question. | The couple should leave a tip of . |

### try it

[ohm_question]146694[/ohm_question]

In the next video we show another example of finding how much tip to give based on percent.

### example

The label on Masao’s breakfast cereal said that one serving of cereal provides milligrams (mg) of potassium, which is of the recommended daily amount. What is the total recommended daily amount of potassium?

[reveal-answer q=”744443″]Show Answer[/reveal-answer]

[hidden-answer a=”744443″]

Solution

What are you asked to find? | the total daily amount of potassium recommended (whole) |

What formula/equation should you use? | |

Substitute in the correct values. | |

Solve. | |

Write a complete sentence that answers the question. | The amount of potassium that is recommended is mg. |

[/hidden-answer]

### try it

[ohm_question]146697[/ohm_question]

[ohm_question]146702[/ohm_question]

### try it

[ohm_question]146703[/ohm_question]

- Revision and Adaptation of DevMath.
**Provided by**: Monterey Institute of Technology and Education.**Located at**: http://www.opentextbookstore.com/arithmetic/arith3-5.pdf.**License**:*CC BY: Attribution*