# Basic Algebra/Proportions and Proportional Reasoning/Percent of Change

## Vocabulary

percent - a ratio that compares a number to 100

percent of change - the percent an amount changes from its original amount.

percent of change = (amount of change) / (original amount), where the amount of change is the new value minus the original value.

percent of increase - when a value increases from its original amount, you call the percent of change the percent of increase

percent of decrease - when a value decreases from its original amount, you call the percent of change the percent of decrease

## Lesson

Finding the percent of change is using the ratio of the amount of change to the original amount. If the amount increases then the percent of change is called the percent of increase and will result in a positive value. If the amount decreases then the percent of change is called the percent of decrease and will result in a negative value.

The first question to ask yourself when finding the percent of change is: Is it an increase or a decrease? Once you have determined what type of change you are dealing with then you can calculate what that percent of change is.

The percent of change is calculated by dividing the amount of change by the original amount. The amount of change is the new value minus the original value. An easy way to remember how to find percent of change is to consider the no over o method. In the no over o method, n stands for the new amount and the o stands for the original amount.

Here is how to use the no over o method.

(the new amount - the original amount) over the original amount.

(n-o)/o

## Example Problems

A. Solve and describe the percent of change as a percent of increase or decrease. Round to the nearest percent.

1) \$12 to \$9

new amount = \$9

original amount = \$12

(n-o)/o

(9-12)/12 = -3/12 = -1/4 = -0.25

no over o is negative which means it decreased so there is a 25% decrease

2) 19 in to 25 in

new amount = 25 in

original amount = 19 in

(n-o)/o

(25-19)/19 = 6/19 = 0.3158

no over o is positive which means it increased so there is approximately a 32% increase

B. Solve the percent of change word problem

1) Anna's grade in Algebra changed from 88 to 94. What is the percent of change in her grade?

new amount = 94

original amount = 88

(n-o)/o

(94-88)/88 = 6/88 = 3/44 = .068 = 6.8%

therefore it was a 6.8% increase

2) Between 1940 and 1980 the Federal budget went from \$725.3 billion to \$9.5 billion. What was the percent of change?

new amount = \$9.5 billion

original amount = \$725.3 billion

(n-o)/o

(9.5-725.3)/725.3 = -715.8/725.3 = -0.986 = -98.6%

therefore it was a 98.6% decrease

C. Solve

1) If 46 is decreased by 20%, what is the result?

new amount = x

original amount = 46

(n-o)/o

(x-46)/46 = -0.20

x-46 = -9.2

x = 36.8

2) If 16 is increased by 30%, what is the result?

new amount = x

original amount = 16

(n-o)/o

(x-16)/16 = 0.30

x-16 = 4.8

x = 20.8

## Practice Problems

Find the percent of change. Describe the percent of change as a percent of increase or decrease. Round your answer to the nearest integer.

1 36 g to 27 g

2 500 lb to 1500 lb

3 \$100 to \$140

4 238 ft to 207 ft

5 18 ft to 50 ft

6 58 to 76

7 100 mi to 175 mi

8 350 to 340

9 64 ft to 48 ft

10 26.2 to 22.8

Find the percent of change

11 If the price of a pen increased from \$100 to \$101, what was the percent of increase?

12 If the price of a softball glove decreased from \$60 to \$36, what was the percent of decrease?

13 Mary decreased her time in the mile walk from 30 minutes to 24 minutes. What was the percent of decrease?

14 A DVD movie originally cost \$24.99. Its current price is \$19.99. What is the percent of change rounded to the nearest percent?

15 A hat's price rose from \$9.99 to \$12.99. What was the percent of change rounded to the nearest percent?

16 Tom's weekly salary increased from \$240 to \$288. What was the percent of change?

17 Kate had \$2,251.35 in her bank account. Currently, she has \$1,975.86 in her account. Find the percent of change rounded to the nearest percent.

18 A car dealer raised the price of a car from \$10,500 to \$11,000. What was the percent of change?

19 In 1986 the average price of a gallon of gasoline was 93 cents. In 2007 the average price of a gallon of gasoline was \$2.77. Find the percent of change.

Solve

20 If 48 was decreased by 20%, what would be the result?

21 What is the result when 50 is decreased by 40%?

22 A \$25 shirt was marked down by 15%. What was the discount?

23 John would like to increase his 140 bowling average by 25%. How many additional pins must he knock down?

24 A shoe store advertises that all shoes are on sale for 30% off the regular price. Find the sale price of a pair of shoes that have an original price of \$85.

25 A toy store prices items 40% over the price paid by the store. If the store purchases a toy truck for \$30, find the selling price of the truck.