Lesson 3-7

Percent of Change

Objectives

• Find the percents of increase and decrease

• Solve problems involving percents of change

Vocabulary

• Percent of change – The expression of an increase or a decrease.

• Percent of increase – occurs when the new number is greater than the old number.

• Percent of decrease – occurs when the new number is less than the old number.

Key Concepts

• Step 1: Explore the Problem

– Identify what information is given (the facts)

– Identify what you are asked to find (the question)

• Step 2: Plan the Solution

– Find an equation the represents the problem

– Let a variable represent what you are looking for

• Step 3: Solve the Problem

– Plug into your equation and solve for the variable

• Step 4: Examine the Solution

– Does your answer make sense?

– Does it fit the facts in the problem?

Example 1

State whether the percent of change is a percent of increase or a percent of decrease. Then find the percent of change.

Find the amount of change. Since the new amount is greater than the original, the percent of change is a percent of increase.

40 – 32 = 8

original: 32new: 40

Example 1 cont

Find the percent using the original number, 32, as the base.

change

original amount

percent change

100 percent

Find the cross products.

Simplify.

Simplify.

Answer: The percent of increase is 25%.

Divide each side by 32.

Example 2

Sales The price a used-book store pays to buy a book is $5. The store sells the book for 28% above the price that it pays for the book. What is the selling price of the $5 book?

Let s = the selling price of the book. Since 28% is the percent of increase, the amount the used-book store pays to buy a book is less than the selling price. Therefore, s – 5 represents the amount of change.

Example 2 cont

Find the cross products.

Distributive Property

Simplify.

Answer: The selling price of the $5 book is $6.40.

change

book store cost

percent change

100 percent

Simplify.

Divide each side by 100.

Add 500 to each side.

Example 3

Sales Tax A meal for two at a restaurant costs 32.75. If the sales tax is 5%, what is the total price of the meal?

The tax is 5% of the price of the meal.

Use a calculator.

Round $1.6375 to $1.64. Add this amount to the original price.

Answer: The total price of the meal is $34.49.

Example 4

The discount is 20% of the original price.

Subtract $0.76 from the original price.

Answer: The discounted price of the dog toy is $3.04.

Discount A dog toy is on sale for20% off the original price. If the original price of the toy is $3.80, what is the discounted price?

Summary & Homework

• Summary:– If the value gets less, then the change is a

decrease; but if the value gets larger, then the change is an increase

– The proportion

is used to find the percents of change (r)

• Homework: – none

amount of change r---------------------------- = ------- original amount 100