6.14: Percent of Increase
Have you ever overheard an adult conversation?
Taylor overheard her Aunt Alicia talking with her Uncle about stocks. Aunt Alicia had 150 shares of XYZ stock. She just bought more shares of the same stock and now has a total of 225 shares.
What is the percent of increase in the number of shares?
You will learn how to find the percent of increase in this Concept. We will revisit the problem at the end of the Concept.
Guidance
Sometimes, we have a price that has been increased a specific amount, or we can observe that over time a price has increased. We think of past pricing in this way.
The cost of a postage stamp has increased over time. In fact, some people think that the cost has increased too much. When we compare a past price and an increased current price, we can figure out the percent that a price has increased. We call this the percent of increase.
How do we calculate 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
Step 1: Find the amount of increase by subtracting the original price from the new price.
Step 2: Write a fraction in which the numerator is the amount of increase and the denominator is the original amount.
\begin{align*}\text{Percent of increase} = \frac{\text{Amount of increase}} {\text{Original amount}}\end{align*}
Step 3: Write the fraction as a percent.
Take a few minutes to write down these steps for finding the Percent of Increase.
Now let's apply these steps..
Find the percent of increase from 20 to 35.
Step 1: Subtract 20 from 35. \begin{align*}35  20 = 15\end{align*}
Step 2: \begin{align*}\text{Percent of increase} = \frac{\text{Amount of increase}}{\text{Original amount}} = \frac{15}{20}\end{align*}
Step 3:
One Way  Another Way 

\begin{align*}\frac{15}{20} = \frac{x}{100}\end{align*} 
\begin{align*}\frac{15}{20} = \frac{15 \div 5}{20 \div 5} = \frac{3}{4}\end{align*} 
\begin{align*}20 x = 1,500\end{align*} 
\begin{align*}\overset{ \ \ 0.75}{4 \overline{ ) {3.00 \;}}} \leftarrow \ \text{Divide to 2 decimal places.}\end{align*} 
\begin{align*}\frac{\cancel{20} x} {\cancel{20}} = \frac{1,500}{20}\end{align*} 
\begin{align*}0.75 = 75 \%\end{align*} 
\begin{align*}x = 75\end{align*} 

\begin{align*}\frac{75}{100} = 75 \%\end{align*} 
The percent of increase from 20 to 35 is 75%.
Notice that we 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.
Find the percent of increase from 24 to 72.
Step 1: Subtract 24 from 72. \begin{align*}72  24 = 48\end{align*}
Step 2: \begin{align*}\text{Percent of increase} = \frac{\text{Amount of increase}}{\text{Original amount}} = \frac{48}{24}\end{align*}
Step 3:
One Way  Another Way 

\begin{align*}\frac{48}{24} = \frac{x}{100}\end{align*} 
\begin{align*}\frac{48}{24} = 2\end{align*} 
\begin{align*}24 x = 4,800\end{align*} 
\begin{align*}2 = 200 \%\end{align*} 
\begin{align*}\frac{\cancel{24} x}{\cancel{24}} = \frac{4,800}{24}\end{align*} 

\begin{align*}x = 200\end{align*} 

\begin{align*}\frac{200}{100} = 200 \%\end{align*} 
The percent of increase from 24 to 72 is 200%.
Yes. Sometimes the percent of increase can be greater than 100%!!
Find the percent of increase. You may round to the nearest whole percent when needed.
Example A
From 45 to 50
Solution: \begin{align*}11%\end{align*}
Example B
From $1.00 to $1.75
Solution: \begin{align*}75%\end{align*}
Example C
From 34 to 60
Solution: \begin{align*}76%\end{align*}
Here is the original problem once again.
Taylor overheard her Aunt Alicia talking with her Uncle about stocks. Aunt Alicia had 150 shares of XYZ stock. She just bought more shares of the same stock and now has a total of 225 shares.
What is the percent of increase in the number of shares?
First, we figure out the amount of the increase by subtracting.
\begin{align*}225  150 = 75\end{align*}
Next, we divide this number by the original amount.
\begin{align*}75 \div 150 = .5\end{align*}
Finally, we can convert the decimal to a percent.
\begin{align*}.5 = 50%\end{align*}
This is the percent of the increase.
Vocabulary
Here is a vocabulary word in this Concept.
 Percent of Increase
 the percent that a price or cost or number has increased.
Guided Practice
Here is one for you to try on your own.
Marcy went from running 15 miles to running 18 miles. What was the percent of the increase?
Answer
First, we have to figure out the amount of the increase. We do this by subtracting.
\begin{align*}18  15 = 3\end{align*}
Now we can use this equation.
\begin{align*}percent of increase = \frac{amount of increase}{original amount}\end{align*}
Next, we fill in the missing values.
\begin{align*}% = \frac{3}{15}\end{align*}
\begin{align*}% = .2\end{align*}
\begin{align*}20%\end{align*}
This is the percent of increase.
Video Review
Here is a video for review.
 This is a James Sousa video on finding a percent of increase.
Practice
Directions: 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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Here you'll learn to find a percent of increase.