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# 6.13: Percent Equation to Find the Base b

Difficulty Level: At Grade Created by: CK-12
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Have you ever watched a hockey game? Well, while it was slow at the candy store, Taylor's Uncle let her watch the game in the office. Here is what happened.

In the hockey game, the Falcons attempted many shots. 15% of shots were goals making 6 goals total.

How many attempts did the team make?

To figure this out you will need to know how to use the percent equation to find base, b. This Concept will teach you how to do this.

### Guidance

When you know the percent and the amount, you can use the equation to find the base, b\begin{align*}b\end{align*}.

Let's look apply the percent equation to this problem.

3 is 50% of what number?

Remember, that the words “of what number” let you know that you are looking for the base.

Let’s fill in the other given information into our equation. First, let’s change the percent to a decimal.

50=.50\begin{align*}50 = .50\end{align*}

Now let’s work on the equation.

3=.50b\begin{align*}3 =.50b\end{align*}

Next, we can use the inverse operation and solve for b\begin{align*}b\end{align*}.

3.506=b=b

The answer is 6.

9 is 75% of what number?

First, let’s change 75% to a decimal.

75% = .75

Next, let’s fill the given values into the equation.

9=.75b\begin{align*}9=.75b \end{align*}

Now we can solve for b\begin{align*}b\end{align*} using the inverse operation.

9.7512=b=b

Our answer is 12.

Find the base for each problem.

#### Example A

8 is 20% of what number?

Solution: 40

#### Example B

15 is 30% of what number?

Solution: 50

#### Example C

22 is 40% of what number?

Solution: 55

Here is the original problem once again.

In the hockey game, the Falcons attempted many shots. 15% of shots were goals making 6 goals total.

How many attempts did the team make?

To figure this out you will need to know how to use the percent equation to find base, b. This Concept will teach you how to do this.

Think: 15% is the percent. Six goals is the number of goals, or part a. How many shots did the team take? This is part b.

First, write the percent as a decimal.

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

Now we can write an equation using this statement.

6 is 15% of what number?

6=.15x\begin{align*}6 = .15x\end{align*}

Now we can use the inverse operation to divide.

6÷.15=x\begin{align*}6 \div .15 = x\end{align*}

40\begin{align*}40\end{align*}

The Falcons made 40 attempts to score their 6 goals.

### 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.

The Cougars basketball team won 21 games. If that number is 70% of the games that the team played, how many games did they play?

Think: 70% is the percent. 21 is the amount of games that they won. You want to find the base.

First, we can take 70% and write it as a decimal.

70%=.70\begin{align*}70\% = .70\end{align*}

Next, we can write the given information into an equation and solve it using the inverse operation.

2121.7030=.70b=b=b

The team played 30 games in all.

### Video Review

Here is a video for review.

### Practice

Directions: Use the percent equation to find each base.

1. 5 is 10% of what number?

2. 15 is 30% of what number?

3. 18 is 20% of what number?

4. 12 is 50% of what number?

5. 15 is 40% of what number?

6. 14 is 20% of what number?

7. 80 is 25% of what number?

8. 60 is 30% of what number?

9. 45 is 40% of what number?

10. 16 is 25% of what number?

11. 60 is 18% of what number?

12. 25 is 30% of what number?

13. 21 is 15% of what number?

14. 55 is 10% of what number?

15. 67 is 20% of what number?

### Vocabulary Language: English

Amount

Amount

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

Base

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

Decimal

In common use, a decimal refers to part of a whole number. The numbers to the left of a decimal point represent whole numbers, and each number to the right of a decimal point represents a fractional part of a power of one-tenth. For instance: The decimal value 1.24 indicates 1 whole unit, 2 tenths, and 4 hundredths (commonly described as 24 hundredths).
Equation

Equation

An equation is a mathematical sentence that describes two equal quantities. Equations contain equals signs.
Inverse Operation

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

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

## Date Created:

Nov 30, 2012

Aug 26, 2015
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