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Percent Equation to Find Part a

Find x% of a number

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Use the Percent Equation to Find Part a

License: CC BY-NC 3.0

Jordan received $85 from his aunts for his birthday. He wants to buy a new game for his computer. His mother told him he could spend no more than 28% of his money on a computer game. How much money can Jordan spend?

In this concept, you will learn to use the percent equation to find part a.

Finding Part a

You can use the proportion \begin{align*}\frac{a}{b} = \frac{p}{100}\end{align*} to solve for a percent. You can also solve percent problems by using an equation. In this concept, you will use a proportion to create a different kind of equation that will help you solve percent problems. 

When you solve the proportion \begin{align*}\frac{a}{b} = \frac{p}{100}\end{align*}, you cross multiply to find the missing variable. You can rearrange this formula so that you are solving for just the variable \begin{align*}a\end{align*}.

\begin{align*}\begin{array}{rcl} \frac{a}{b} &=& \frac{p}{100} \\ 100a &=& pb \\ \frac{100a}{100} &=& \frac{pb}{100} \\ a&=&\frac{pb}{100} \end{array}\end{align*} You could also say that \begin{align*}a= \frac{pb}{100}\end{align*} is equal to \begin{align*}a = 0.01 pb\end{align*}. As well, you could convert your percent directly into a decimal and therefore the formula becomes even simpler.

Let’s look at an example.

What is 85% of 90?

First, change the 85% into a decimal. You know that percent means that the denominator of the fraction is 100.

Therefore, \begin{align*}85\% = 0.85\end{align*}.

Next, multiply using the percent equation.

\begin{align*} \begin{array}{rcl} a &=& 0.01 pb \\ a &=& 0.85 \times 90 \\ a &=& 76.5 \\ \end{array}\end{align*}The answer is 76.5.

Let’s look at another example.

What is 7% of 900?

First, change the 7% into a decimal. You know that percent means that the denominator of the fraction is 100.

Therefore, \begin{align*}7\% = 0.07\end{align*}.

Next, multiply using the percent equation.

\begin{align*}\begin{array}{rcl} a &=& 0.01 pb \\ a &=& 0.07 \times 900 \\ a &=& 63 \end{array}\end{align*} The answer is 63.

Examples

Example 1

Earlier, you were given a problem about Jordan and his partial spending money.

Jordan has $85 from his birthday but cannot spend any more than 28% of it on his new computer game. How much can he spend?

First, change the 28% into a decimal.

\begin{align*}28\% = 0.28\end{align*}

Next, multiply using the percent equation.

\begin{align*}\begin{array}{rcl} a &=& 0.01 pb \\ a &=& 0.28 \times 85 \\ a &=& 23.8 \end{array}\end{align*} The answer is 23.8.

Therefore, Jordan can spend up to $23.80 on his new computer game.

Example 2

What is 19% of 300?

First, change the 19% into a decimal.

\begin{align*}19\% = 0.19\end{align*}

Next, multiply using the percent equation.

\begin{align*}\begin{array}{rcl} a &=& 0.01 pb \\ a &=& 0.19 \times 300 \\ a &=& 57 \end{array}\end{align*} The answer is 57.

Example 3

What is 22% of 100?

First, change the 22% into a decimal.

\begin{align*}22\% = 0.22\end{align*}

Next, multiply using the percent equation.

\begin{align*} \begin{array}{rcl} a &=& 0.01 pb \\ a &=& 0.22 \times 100 \\ a &=& 22 \end{array}\end{align*} 

The answer is 22.

Example 4

What is 8% of 57?

First, change the 8% into a decimal.

\begin{align*}8\% = 0.08\end{align*}

Next, multiply using the percent equation.

\begin{align*}\begin{array}{rcl} a &=& 0.01 pb \\ a &=& 0.08 \times 57 \\ a &=& 4.56 \end{array}\end{align*}

The answer is 4.56.

Example 5

What is 17% of 80?

First, change the 17% into a decimal.

\begin{align*}17\% = 0.17\end{align*}

Next, multiply using the percent equation.

\begin{align*} \begin{array}{rcl} a &=& 0.01 pb \\ a &=& 0.17 \times 80 \\ a &=& 13.6 \end{array}\end{align*} The answer is 13.6.

Review

Solve each percent problem. Round your answers to the nearest tenth when necessary.

  1. How much is 15% of 73?
  2. What is 70% of 5?
  3. What is 3% of 4 million?
  4. What is 18% of 30?
  5. What is 22% of 56?
  6. What is 19% of 300?
  7. What is 21% of 45?
  8. What is 34% of 250?
  9. What is 33% of 675?
  10. What is 3% of 700?
  11. What is 11% of 955?
  12. What is 14% of 55?
  13. What is 37% of 17?
  14. What is 20% of 9?
  15. What is 2% of 18?

Review (Answers)

To see the Review answers, open this PDF file and look for section 5.7. 

Resources

 

Vocabulary

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).

Inverse Operation

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

Proportion

A proportion is an equation that shows two equivalent ratios.

Image Attributions

  1. [1]^ License: CC BY-NC 3.0

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