Has the attendance at your school ever changed? Take a look at this dilemma.

Cameron and Carla decided to bring their proposal of increased attendance to the student council. They thought that if the student council suggested an increase in attendance to the student body that students might really want to help out.

“We know that 100% attendance is nearly impossible, but we could get to 55 or 60%, I think,” Cameron suggested.

“Then we could really show the high school that we support their efforts,” Carla chimed in.

“I think it is a great idea,” Avery, the President of the student council said. “We could conduct a survey and see how many students anticipate attending. Then we could try to predict the number of students who will attend next fall.”

That is exactly what they did. The students conducted a survey and asked students if they would be willing to attend next year’s football games to support the high school team. Out of their survey, they learned that 198 students said they planned on attending. That is an increase from 152 students. What is the percent of the increase?

**This is the question for this Concept. Percents of increase are often used in real – life situations. Work through the content of this Concept and by the end you will be able to figure out the percent of the increase if the survey proves true.**

### Guidance

Many times in the real world, things change—prices go up and down, your bank account balances go up and down, your weight goes up and down, businesses get more or less business, we have more hurricanes and typhoons than before, etc. Interpreting the amount of change as a percent is oftentimes useful to understand a situation and compare it to others.

**Let’s look at percent of increase first.**

**Two years ago, Mingh was 116 cm tall. She is now 132 cm tall. Her height increased by 16 cm in two years. Two years ago, her little brother Charlie was only 80 cm tall. He has grown to 95 cm... almost a full meter! He grew 15 cm. Which one grew more?**

Let’s start to work on this problem. In the beginning, it might seem obvious that Mingh grew more—she grew 16 cm and Charlie only grew 15 cm. But if we consider the percent of increase, we might have a different argument.

**What is the percent of increase?**

The *percent of increase* is the percent that something value increased.

How does that apply to this problem?

First, we have to figure out what the percent of increase was in growth for both children. Mingh grew 16cm. Her original height was 116cm. What percent did she increase?

If we consider 16cm the part of her original height that she increased, we can find percent of increase by using the ratio \begin{align*}\frac{16}{116}=.138\end{align*} or 13.8%. We divide the amount of increase by the original amount and change to a percent by multiplying by 100 (or moving the decimal point two places to the right).

Mingh’s height increased by 13.8%.

What was Charlie’s percent of increase?

His height increased by 15cm but his original height was only 95cm. So his percent of increase was \begin{align*}\frac{15}{95}=.158\end{align*} or 15.8%. So although Mingh grew 1cm more than Charlie, Charlie increased by 15.8% while Mingh increased by only 13.8%.

**So we might argue that Charlie grew more than Mingh because his percent of increase was greater.**

**We can find any** *percent of increase***by dividing the amount of increase by the original amount and then multiplying by 100.**

** Write this down in your notebook.** In the last 3 years, the price of gas has risen from an average of $1.89 per gallon to an average of $2.95 per gallon. This is an increase of $1.06 per gallon. What is the percent of increase?

**To solve for this percent of increase, we divide the amount of the increase by the original amount and multiply by 100. In this case, the increase was $1.06.**

\begin{align*}\frac{1.06}{1.89} = .561 = 56.1 \% \ increase\end{align*}

**56.1% is our answer.**

*Notice that we multiply by 100 to convert the decimal into a percent since we are looking for the “percent of increase.”*

Find the percent of increase for each example.

#### Example A

From 10 to 45.

**Solution: \begin{align*}350\%\end{align*}**

#### Example B

From 15 to 20.

**Solution: \begin{align*}33.3\%\end{align*}**

#### Example C

From 80 to 360.

**Solution: \begin{align*}350\%\end{align*}**

Now let's go back to the dilemma from the beginning of the Concept.

**To solve for the percent of increase, we first need to figure out the difference between the old attendance and the predicted new attendance.**

**The old attendance = 152 students**

**The new attendance = 198 students**

\begin{align*}198 - 152 = 46 \end{align*}

**Next, we put that difference over the original attendance.**

\begin{align*}\frac{46}{152}\end{align*}

**Now we divide.**

.302 = 30.2%

**If the prediction of the students is true, than it would be a 30% increase in attendance.**

### Vocabulary

- Percent
- a part of a whole out of 100.

- Percent of Increase
- the percent of change that a value increased.

### Guided Practice

Here is one for you to try on your own.

A tree grew 2 inches every year. When Mary first planted the tree, it was 6 inches tall. After 10 years, it was 26 inches tall. What was the percent of increase from year 10 to when Mary first planted the tree?

**Solution**

First, find the difference.

\begin{align*}26 - 6 = 20\end{align*}

Now divided 20 by the original amount.

\begin{align*}\frac{20}{6} = 3.33\end{align*}

Next, multiply by 100. We can accomplish this task by moving the decimal point.

\begin{align*}333\%\end{align*}

**This is the percent of the increase.**

### Video Review

Determine a Percent of Increase

### Practice

Directions: Calculate the percent of increase. You may round to the nearest whole percent.

- From 7 to 12, an increase of 5
- From 31 to 50, an increase of 19
- From 7805 to 10510, an increase of 2705
- From 16 to 30, an increase of 14
- From 200 to 230, an increase of 30
- From 180 to 200
- From 330 to 400
- From 695 to 1000
- From 1200 to 1500
- From 190 to 320
- From 90 to 120
- From 110 to 120
- From 340 to 350
- From 670 to 1000
- From 879 to 900