# 6.6: Proportions to Find Part a

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

**Practice**Proportions to Find Part a

Jamal works at a local store after school that sells pumpkin lanterns for $12. The day after Halloween, the store manager wants Jamal to mark down the lanterns by 75%. What new price sticker does Jamal put on them?

In this concept, you will learn to use a proportion to find part \begin{align*}a\end{align*}, the amount.

### Proportions to Find the Amount

Sometimes you will be given the base and the percent, and you will need to find the amount. You can use the same proportion to figure out this missing value, \begin{align*}a\end{align*}. You just need to fill in the numbers in the correct places and solve.

Let’s look at an example.

What is 25% of 75?

To figure this out, let’s look at what you have been given for information. First, you know the percent so you can fill in that half of the proportion.

\begin{align*}\frac{25}{100}\end{align*}

Next, you have been given the base. “Of 75” lets you know that this number is the base. The amount is missing. That is our unknown. So the second half of the proportion is:

\begin{align*}\frac{a}{75}\end{align*}

Now let’s put it together as a proportion and use cross products to solve for \begin{align*}a\end{align*}.

\begin{align*}\begin{array}{rcl} \frac{a}{75} & = & \frac{25}{100}\\ 100a & = & 75(25)\\ 100a & = & 1875\\ a & = & 18.75 \end{array}\end{align*}

Notice that you moved the decimal point two places to the left when you divided by 100.

The answer is 18.75 or \begin{align*}18 \frac{3}{4}\end{align*} is 25% of 75.

Notice that there isn’t a percent sign here because you were looking for an amount not a percent. Remember to note what you are looking for.

Let’s take a look at another example.

What number is 15% of 60?

First, set up a proportion. Remember, the missing part is variable \begin{align*}a\end{align*}, the amount.

\begin{align*}\frac{a}{60} = \frac{15}{100}\end{align*}

Next, cross-multiply and solve.

\begin{align*}\begin{array}{rcl} 100a & = & 900\\ a & = & 9 \end{array}\end{align*}

The answer is 9 is 15% of 60.

### Examples

#### Example 1

Earlier, you were given a problem about Jamal and his job at the store.

He needs to put discounted price stickers on the Halloween lanterns. The lanterns, which originally cost $12, are now going to be reduced by 75%. What new price sticker does Jamal put on them?

First, if the lanterns are discounted by 75%, their new price is \begin{align*}100\% - 75\%\end{align*} or 25% of the original price.

Next, let’s setup the proportion.

\begin{align*}\frac{a}{12} = \frac{25}{100}\end{align*}

Now you can use cross products to solve for the amount.

\begin{align*}\begin{array}{rcl} 100a & = & 25(12)\\ 100a & = & 300\\ a & = & 3 \end{array}\end{align*}

The answer is the discounted sticker price Jamal should put on the lanterns is $3.

#### Example 2

Mr. Green bought both vegetable and flowering plants for his garden. He bought 40 plants and 35% were flowering plants. How many flowering plants did he buy?

You can think of this problem as “What is 35% of 40?”

40 is the base \begin{align*}(b)\end{align*} and 35 is the percent \begin{align*}(p)\end{align*}. You need to find the amount \begin{align*}(a)\end{align*}.

First, set up the proportion.

\begin{align*}\frac{a}{40} = \frac{35}{100}\end{align*}

Then, use cross products to solve for the amount.

\begin{align*}\begin{array}{rcl} 100a & = & 35(40)\\ 100a & = & 1,400\\ a & = & 14 \end{array}\end{align*}

The answer is Mr. Green bought 14 flowering plants.

#### Example 3

What is 20% of 30?

First, let’s set up the proportion.

\begin{align*}\frac{a}{30} = \frac{20}{100}\end{align*}

Now you can use cross products to solve for the amount.

\begin{align*}\begin{array}{rcl} 100a & = & 20(30)\\ 100a & = & 600\\ a & = & 6 \end{array}\end{align*}

The answer is 6 is 20% of 30.

#### Example 4

What is 16% of 50?

First, let’s set up the proportion.

\begin{align*}\frac{a}{50} = \frac{16}{100}\end{align*}

Now you can use cross products to solve for the amount.

\begin{align*}\begin{array}{rcl} 100a & = & 16(50)\\ 100a & = & 80\\ a & = & 8 \end{array}\end{align*}

The answer is 8 is 16% of 50.

#### Example 5

What is 22% of 80?

First, let’s set up the proportion.

\begin{align*}\frac{a}{80} = \frac{22}{100}\end{align*}

Now you can use cross products to solve for the amount.

\begin{align*}\begin{array}{rcl} 100a & = & 22(80)\\ 100a & = & 1,760\\ a & = & 17.6 \end{array}\end{align*}

The answer is 17.6 is 22% of 80.

### Review

Find each missing amount.

- What number is 25% of 18?
- What number is 10% of 20?
- What number is 45% of 16?
- What number is 20% of 44?
- What number is 30% of 100?
- What number is 25% of 60?
- What number is 40% of 80?
- What number is 40% of 60?
- What number is 50% of 120?
- What number is 5% of 12?
- What number is 5% of 20?
- What number is 16% of 80?
- What number is 25% of 23?
- What number is 50% of 17?
- What number is 30% of 33?

### Review (Answers)

To see the Review answers, open this PDF file and look for section 6.6.

### Resources

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In this concept, you will learn to use a proportion to find part a, the amount.

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