# 6.12: Percent Equation to Find Percent

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

**Practice**Percent Equation to find Percent

Shelly bought a bouquet for her teacher at the flower shop. She counted 9 red roses and 12 pink roses in the bouquet. What percent of the roses are red and what percent are pink?

In this concept, you’ll learn how to use the percent equation to find \begin{align*}p\end{align*}, the percent.

### Using the Percent Equation to Find the Percent

You can use the percent equation to find the percent, \begin{align*}p\end{align*}, of a number. When you look at this type of problem, you will be given the amount and the base, but the percent will be a mystery. Let’s think about how to solve for the percent using the percent equation.

Here is the percent equation once again.

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

Now let’s look at how to apply this equation.

What percent of 70 is 14?

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

\begin{align*}\begin{array}{rcl} a &=& p \times b\\ 14 &=& p (70) \end{array}\end{align*}

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

\begin{align*}\begin{array}{rcl} \frac{14}{70} &=& p\%\\ 0.2 &=& p\% \end{array}\end{align*}

Now, change the decimal to a percent.

The answer 14 is 20% of 70.

You must change the decimal to a percent when you are looking for a percent.

### Examples

#### Example 1

Earlier, you were given a problem about Shelley and her bouquet.

12 of the roses in the bouquet were pink and 9 of the roses were red. What percent of the roses were pink and what percent were red?

First, find the total number of roses in the bouquet: \begin{align*}9 + 12 = 21\end{align*}. This is the base, \begin{align*}b\end{align*}.

Then, write the following equation.

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

Next, fill in the given values, first for the pink roses and then for the red roses.

\begin{align*}12 = 21p\% \ \ \ \text{AND} \ \ \ 9=21p\%\end{align*}

Now, divide both sides by 21.

\begin{align*}\begin{matrix} 12 \div 21 & = & 21p \div 21 & \text{AND} & 9 \div 21 & = & 21p \div 21\\ 0.5714 & = & p & \text{AND} & 0.4286 & = & p \end{matrix}\end{align*}

Next, convert these two decimals to percents.

The answer is 57.14% of the roses in the bouquet are pink and 42.86% of them are red.

#### Example 2

What percent of 250 is 130?

To figure this out, you can first write the following equation.

\begin{align*}a = p \times b\end{align*}Next, fill in the given values.

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

Now, divide both sides by 250.

\begin{align*}\begin{array}{rcl} 130 \div 250 &=& 250p \div 250\\ 0.52 &=& p \end{array}\end{align*}

Next, convert 0.52 to a percent.

The answer is 130 is 52% of 250.

**For the following examples, use the equation to find the missing percent. You may round when necessary.**

#### Example 3

What percent of 50 is 15?

First, write the percent equation.

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

Next, fill in the given values.

\begin{align*}15 = 50p\end{align*}

Now, divide both sides by 50.

\begin{align*}\begin{array}{rcl} 15 ÷ 50 &=& 50p÷ 50\\ 0.30 &=& p \end{array}\end{align*}

Next, convert 0.30 to a percent.

The answer is 15 is 30% of 50.

#### Example 4

What percent of 80 is 25?

First, write the percent equation.

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

Next, fill in the given values.

\begin{align*}25 = 80p \end{align*}

Now, divide both sides by 80.

\begin{align*}\begin{array}{rcl} 25 \div 80 &=& 80p \div 80\\ 0.3125 &=& p \end{array}\end{align*}

Next, convert 0.3125 to a percent.

The answer is 25 is 31.25% of 80.

#### Example 5

What percent of 100 is 12?

First, write the percent equation.

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

Next, fill in the given values.

\begin{align*}12 = 100p\end{align*}

Now, divide both sides by 100.

\begin{align*}\begin{array}{rcl} 12 ÷ 100 &=& 100p÷ 100\\ 0.12 &=& p \end{array}\end{align*}

Next, convert 0.12 to a percent.

The answer is 12 is 12% of 100.

### Review

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

- What percent of 18 is 9?
- What percent of 20 is 10?
- What percent of 60 is 15?
- What percent of 80 is 20?
- What percent of 25 is 10?
- What percent of 70 is 35?
- What percent of 36 is 18?
- What percent of 100 is 25?
- What percent of 10 is 5?
- What percent of 98 is 90?
- What percent of 100 is 14?
- What percent of 200 is 90?
- What percent of 150 is 99?
- What percent of 125 is 88?
- What percent of 133 is 13?

### Review (Answers)

To see the Review answers, open this PDF file and look for section 6.12.

### Resources

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Amount

In a proportion, the amount is the part of the base that is being calculated.Base

In the context of the percent equation, the base is the part of the whole from which the amount is calculated.Inverse Operation

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

Percent means out of 100. It is a quantity written with a % sign.### Image Attributions

In this concept, you will learn how to use the percent equation to find p, the percent.

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