# 6.11: Percent Equation to Find Part a

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

**Practice**Percent Equation to Find Part a

Do you like jelly beans? Take a look at this dilemma.

Taylor’s younger brother Max decided to visit her at the candy store. Max is only seven and can be a handful sometimes, so while Taylor loves to see him, she was a little hesitant to have him in the shop. Plus, what seven year old doesn’t love candy.

Taylor gave Max a small bag to put some candy in. She figured he would take a few pieces, but ended up with a whole bunch of candy.

“How many did you take?” Taylor asked him looking in the bag.

“I took 40 pieces,” Max said grinning. “I won’t eat it all now. I will save some for later.”

Taylor looked into the bag. There were candy canes, peanut butter cups and a whole bunch of jelly beans.

She gave Max the bag and watched him walk away chewing.

“I hope I don’t get into trouble for this,” Taylor murmured to herself.

In looking in the bag, Taylor discovered that 15% of Max's bag was peanut butter cups. If he put 40 pieces of candy in his bag, how many pieces of candy were peanut butter cups?

We can say this another way using a percent equation.

What is 15% of 40?

**This Concept will teach you how to use the percent equation to find part a. Then we will come back to this dilemma at the end of the Concept.**

### Guidance

Think about the proportion that you just learned to find the percent of a number.

\begin{align*}\frac{a}{b}=\frac{p}{100}\end{align*}

When we used this proportion in problem solving, we multiplied \begin{align*}b\end{align*} and \begin{align*}p\end{align*} and \begin{align*}a\end{align*} and 100. Then we divided the product of \begin{align*}b\end{align*} and \begin{align*}p\end{align*} by 100.

Let's look at a statement that uses this proportion.

What is 35% of 6?

**First, we fill in the proportion.**

\begin{align*}\frac{a}{6}=\frac{35}{100}\end{align*}

**Next, we multiply and solve for \begin{align*}a\end{align*}.**

\begin{align*}100a & = 35(6)\\ 100a & = 210\\ a & = 2.1\end{align*}

**Notice that by dividing by 100, we moved the decimal place two places.**

**Hmmmm. This is the same two places that the percent is represented by. This means that if we changed the percent to a decimal FIRST, that we could skip a step and use an equation to find the missing value.**

Take a look at the same problem.

What is 35% of 6?

**First, change 35% to a decimal.**

\begin{align*}35\% = .35\end{align*}

**Now we multiply it times 6, the base and find \begin{align*}a\end{align*} the amount. Look at this equation.**

\begin{align*}a & = p\%(b)\\ a & = .35(6) \\ a & = 2.1 \end{align*}

**Notice that we got the same answer as when we used the proportion. It just simplifies the process.**

Let’s look at another one.

What is 25% of 50?

**First, change 25% to a decimal.**

\begin{align*}25\% = .25\end{align*}

**Now use the equation.**

\begin{align*}a & = p\%(b)\\ a & =.25(50)\\ a & =12.5 \end{align*}

**The answer is 12.5.**

Use the equation to find each amount. Include decimals in your answer.

#### Example A

What is 20% of 16?

**Solution: \begin{align*}3.2\end{align*}**

#### Example B

What is 5% of 40?

**Solution:\begin{align*}2\end{align*}**

#### Example C

What is 15% of 65?

**Solution:\begin{align*}9.75\end{align*}**

Here is the original problem once again.

Taylor’s younger brother Max decided to visit her at the candy store. Max is only seven and can be a handful sometimes, so while Taylor loves to see him, she was a little hesitant to have him in the shop. Plus, what seven year old doesn’t love candy.

Taylor gave Max a small bag to put some candy in. She figured he would take a few pieces, but ended up with a whole bunch of candy.

“How many did you take?” Taylor asked him looking in the bag.

“I took 40 pieces,” Max said grinning. “I won’t eat it all now. I will save some for later.”

Taylor looked into the bag. There were candy canes, peanut butter cups and a whole bunch of jelly beans.

She gave Max the bag and watched him walk away chewing.

“I hope I don’t get into trouble for this,” Taylor murmured to herself.

In looking in the bag, Taylor discovered that 15% of Max's bag was peanut butter cups. If he put 40 pieces of candy in his bag, how many pieces of candy were peanut butter cups?

We can say this another way using a percent equation.

What is 15% of 40?

To figure this out, we can convert 15% into a decimal.

\begin{align*}15% = .15\end{align*}

Next, we multiply .15 by 40.

\begin{align*}40 \times .15 = 6\end{align*}

**Six pieces of candy in the bag were peanut butter cups.**

### 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 is 32% of 200?

**Answer**

To figure this out, first we change the percent to a decimal.

\begin{align*}32% = .32\end{align*}

Next, we multiply this decimal by 200.

\begin{align*}200 \times .32 = 64\end{align*}

**32% of 200 is 64.**

### Video Review

Here is a video for review.

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

### Practice

Directions: Use the percent equation to find each amount.

1. What is 20% of 18?

2. What is 10% of 30?

3. What is 5% of 90?

4. What is 12% of 27?

5. What is 18% of 30?

6. What is 50% of 88?

7. What is 75% of 12?

8. What is 75% of 90?

9. What is 22% of 40?

10. What is 25% of 60?

11. What is 8% of 15?

12. What is 99% of 200?

13. What is 90% of 12?

14. What is 18.5% of 230?

15. What is 20.5% of 160?

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### Image Attributions

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