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.

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

### Review (Answers)

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

### Resources

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