# 6.12: Percent Equation to Find Percent

**At Grade**Created by: CK-12

On Saturday, Taylor’s parents decided to have a big sale at the candy store. They advertised in the local newspapers and on Saturday morning they were ready for a big crowd. Taylor was responsible for counting all of the people who came into the store between 10 am when they opened and Noon.

Taylor sat on a stool at the front of the store and counted people as they came in. She was pleasant and enjoyed seeing all of the different shoppers. She only counted adults or teenagers not little kids with their parents since most parents would be doing the buying instead of the little children. Most people bought something, but a few just came in to look around.

At lunch, she compared her data with her brother Henry who was helping with the sales at the cash register.

“How many people did you count?” Henry asked.

“I counted 30 adults. How many sales were there?”

“There were 24 sales.”

“That’s not bad. Most people bought something. What percent ended up buying something?” Taylor asked Henry.

Just as Henry was about to answer her, he got called back into the store. Taylor sat there eating her sandwich thinking about the percentages.

What percent of the people who came into the store made a purchase?

What percent did not purchase anything?

**In this Concept, you will learn how to use an equation to solve problems like this one. Pay attention and at the end you will be able to help Taylor with the problem.**

### Guidance

We can use the percent equation from the last Concept to find the percent of a number. When you look at this problem, you will be given the amount and the base, but the percent will be a mystery. Let’s think about how to do this.

**Here is the percent equation once again.**

\begin{align*}a=p\% b\end{align*}

Now let’s look at how to apply this.

What percent of 70 is 14?

**First, we have the \begin{align*}a\end{align*} and the \begin{align*}b\end{align*} and we are missing the percent. We can fill the given information into the formula.**

\begin{align*}a& =pb \\ 14& =p70 \end{align*}

**Now we can figure out what number times seventy is 14. Since the operation is multiplication, we can do the opposite and divide. This is using the** *inverse operation.*

\begin{align*}\frac{14}{70}& =p \\ .2 & = p\end{align*}

**Now we change the decimal to a percent.**

**Our answer is 20%.**

**Don’t forget to change the decimal to a percent when you are looking for a percent!!**

Use the equation to find the missing percent. You may round when necessary.

#### Example A

What percent of 50 is 15?

**Solution: \begin{align*}30%\end{align*}**

#### Example B

What percent of 80 is 25?

**Solution: \begin{align*}31%\end{align*}**

#### Example C

What percent of 100 is 12?

**Solution: \begin{align*}12%\end{align*}**

Here is the original problem once again. Use what you have learned to solve this problem.

On Saturday, Taylor’s parents decided to have a big sale at the candy store. They advertised in the local newspapers and on Saturday morning they were ready for a big crowd. Taylor was responsible for counting all of the people who came into the store between 10 am when they opened and Noon.

Taylor sat on a stool at the front of the store and counted people as they came in. She was pleasant and enjoyed seeing all of the different shoppers. She only counted adults or teenagers not little kids with their parents since most parents would be doing the buying instead of the little children. Most people bought something, but a few just came in to look around.

At lunch, she compared her data with her brother Henry who was helping with the sales at the cash register.

“How many people did you count?” Henry asked.

“I counted 30 adults. How many sales were there?”

“There were 24 sales.”

“That’s not bad. Most people bought something. What percent ended up buying something?” Taylor asked Henry.

Just as Henry was about to answer her, he got called back into the store. Taylor sat there eating her sandwich thinking about the percentages.

What percent of the people who came into the store made a purchase?

What percent did not purchase anything?

**First, notice that we are looking for a percent.**

30 is the base and 24 is the amount. Let’s fill in the given information and solve for the percent that did purchase at the store.

\begin{align*}24& =30p\\ \frac{24}{30}& =p\\ .8 & = p\\ 80\% & = p\end{align*}

**80% purchased something at the store.**

**What percent did not purchase something?**

100% - 80% = 20%

**20% did not purchase anything at the store.**

### Vocabulary

Here are the vocabulary words in this Concept.

- Inverse Operation
- the opposite operation.

- Percent
- a part of a whole calculated out of 100.

- Amount
- the part of the whole that “is” out of a base. “Is” is a key word showing amount.

- Base
- the part of the whole that the amount is out of. The word “Of what number” let you know that you are looking for the base.

### Guided Practice

Here is one for you to try on your own.

What percent of 250 is 130?

**Answer**

To figure this out, we can write the following equation.

\begin{align*}250p = 130\end{align*}

Now we divide 130 by 250.

\begin{align*}130 \div 250 = .52\end{align*}

Next, we convert \begin{align*}.52\end{align*} to a percent.

**The answer is \begin{align*}52%\end{align*}.**

### Video Review

Here is a video for review.

- This is a James Sousa video on using the percent equation to find the percent.

### Practice

Directions: Use the percent equation to find each percent. You may round your answer to the nearest whole percent if necessary.

1. What percent of 18 is 9?

2. What percent of 20 is 10?

3. What percent of 60 is 15?

4. What percent of 80 is 20?

5. What percent of 25 is 10?

6. What percent of 70 is 35?

7. What percent of 36 is 18?

8. What percent of 100 is 25?

9. What percent of 10 is 5?

10. What percent of 98 is 90?

11. What percent of 100 is 14?

12. What percent of 200 is 90?

13. What percent of 150 is 99?

14. What percent of 125 is 88?

15. What percent of 133 is 13?

### Image Attributions

Here you'll use the percent equation to find the percent.