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# 6.14: Percent of Increase

Difficulty Level: At Grade Created by: CK-12
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On March 8, 2010, Cento Coffee Shop began charging $2.50 for its drip coffee. Prior to that date, the shop charged$2.25 for its drip coffee. What was the percent increase in the drip coffee’s cost on March 8, 2010?

In this concept, you will learn how to find the percent of increase.

### Finding Percent of Increase

Sometimes, you will have a price that has been increased by a specific amount. Other times you can observe that a price has increased over time. Past pricing is often thought of in this way. When you compare a past price and an increased current price, you can figure out the percent by which a price has increased. You call this percent the percent of increase.

The percent of increase from one amount to another is the ratio of the amount of increase to the original amount.

To find the percent of increase, follow these steps.

First, find the amount of increase by subtracting the original price from the new price.

Next, write a fraction in which the numerator is the amount of increase and the denominator is the original amount.

Percent of increase=Amount of IncreaseOriginal Amount\begin{align*}\text{Percent of increase} = \frac{\text{Amount of Increase}} {\text{Original Amount}}\end{align*}

Then, write the fraction as a percent.

Now let’s apply these steps.

Find the percent of increase from 20 to 35.

First, subtract 20 from 35.

3520=15\begin{align*}35 - 20 = 15\end{align*}

Next, write the fraction: Percent of increase=Amount of IncreaseOriginal Amount=1520\begin{align*}\text{Percent of increase} = \frac{\text{Amount of Increase}} {\text{Original Amount}} = \frac{15}{20}\end{align*}

Then:

One Way

152020x20x20x====x1001,5001,5002075\begin{align*}\begin{array}{rcl} \frac{15}{20}&=&\frac{x}{100} \\ 20x &=& 1,500 \\ \frac{\cancel{20}x}{\cancel{20}} &=& \frac{1,500}{20} \\ x &=& 75 \end{array}\end{align*}Another Way

1520=15÷520÷5=344)3.00¯¯¯¯¯¯¯¯¯¯¯¯  0.75Divide to 2 decimal places.0.75=75%\begin{align*}&\frac{15}{20}=\frac{15 \div 5}{20 \div 5}=\frac{3}{4} \\ & \overset{ \ \ 0.75}{4 \overline{ ) {3.00 \;}}} \quad \leftarrow \text{Divide to} \ 2 \ \text{decimal places.} \\ &0.75 = 75 \%\end{align*}

The answer is the percent of increase from 20 to 35 is 75%.

Notice that you could solve for the percent in two different ways. One was to use a proportion and the other was to simply divide. Either way, you will get the same answer.

### Examples

#### Example 1

Earlier, you were given a problem about Cento Coffee House.

On March 8, 2010, the price of a drip coffee went from $2.25 to$2.50. What was the percent increase in the drip coffee’s cost?

First, figure out the amount of the increase by subtracting.

2.502.25=0.25\begin{align*}2.50 - 2.25 = 0.25\end{align*}

Next, divide this number by the original amount.

0.25÷2.25=0.11\begin{align*}0.25 \div 2.25 = 0.11\end{align*}

Finally, convert the decimal to a percent.

0.11=11%\begin{align*}0.11 = 11\%\end{align*}

The answer is the price of the drip coffee increased by 11%.

#### Example 2

Let’s look at another example.

Find the percent of increase from 24 to 72.

First, subtract 24 from 72.

7224=48\begin{align*}72 - 24 = 48\end{align*}

Next, write the fraction: Percent of increase=Amount of IncreaseOriginal Amount=4824\begin{align*}\text{Percent of increase} = \frac{\text{Amount of Increase}} {\text{Original Amount}} = \frac{48}{24}\end{align*}

Then:

One Way

482424x24x24x====x1004,8004,80024200\begin{align*}\begin{array}{rcl} \frac{48}{24}&=&\frac{x}{100} \\ 24x &=& 4,800 \\ \frac{\cancel{24}x}{\cancel{24}} &=& \frac{4,800}{24} \\ x &=& 200 \end{array}\end{align*}

Another Way

48242==48÷2424÷24=21200%\begin{align*}\begin{array}{rcl} \frac{48}{24}&=&\frac{48 \div 24}{24 \div 24}=\frac{2}{1} \\ 2 &=& 200 \% \end{array}\end{align*}

The answer is the percent increase from 24 to 72 is 200%.

Yes, sometimes the percent of increase can be greater than 100%!

#### Example 3

Find the percent of increase from 45 to 50. You may round to the nearest whole percent when needed.

First, subtract 45 from 50.

5045=5\begin{align*}50 - 45 = 5\end{align*}

Next, write the fraction: Percent of increase=Amount of IncreaseOriginal Amount=545\begin{align*}\text{Percent of increase} = \frac{\text{Amount of Increase}} {\text{Original Amount}} = \frac{5}{45}\end{align*}

Then solve the proportion:

54545xx===x10050011.11\begin{align*}\begin{array}{rcl} \frac{5}{45} &=& \frac{x}{100} \\ 45x &=& 500 \\ x &=& 11.11 \end{array}\end{align*}

The answer is rounded to the nearest whole percent, the percent increase from 45 to 50 is 11%.

#### Example 4

Find the percent of increase from $1.00 to$1.75. You may round to the nearest whole percent when needed.

First, subtract 1.00 from 1.75.

1.751.00=0.75\begin{align*}1.75 - 1.00 = 0.75\end{align*}

Next, write the fraction: Percent of increase=Amount of IncreaseOriginal Amount=0.751.00\begin{align*}\text{Percent of increase} = \frac{\text{Amount of Increase}} {\text{Original Amount}} = \frac{0.75}{1.00} \end{align*}

Then, divide:

0.751.00=0.75=75%\begin{align*}\frac{0.75}{1.00} = 0.75 = 75 \%\end{align*}

The answer is the percent increase from $1.00 to$1.75 is 75%.

#### Example 5

Find the percent of increase from 34 to 60. You may round to the nearest whole percent when needed.

First, subtract 34 from 60.

6034=26\begin{align*}60 - 34 = 26\end{align*}

Next, write the fraction: Percent of increase=Amount of IncreaseOriginal Amount=2634\begin{align*}\text{Percent of increase} = \frac{\text{Amount of Increase}} {\text{Original Amount}} = \frac{26}{34}\end{align*}

Then, solve the proportion:

263434xx===x1002,60076.47\begin{align*}\begin{array}{rcl} \frac{26}{34} &=& \frac{x}{100} \\ 34x &=& 2,600 \\ x &=& 76.47 \end{array} \end{align*}The answer is rounded to the nearest whole percent, the percent increase from 34 to 60 is 76%.

### Review

Find the percent of increase given the original amount. You may round to the nearest whole percent when necessary.

1. From 25 to 40
2. From 15 to 30
3. From 18 to 50
4. From 22 to 80
5. From 16 to 18
6. From 3 to 10
7. From 85 to 100
8. From 75 to 90
9. From 26 to 36
10. From 100 to 125
11. From 100 to 150
12. From 125 to 175
13. From 175 to 200
14. From 200 to 225
15. From 225 to 275

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### Vocabulary Language: English

Percent of Increase

The percent of increase is the percent that a value has increased by.

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