Download Lesson 7

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.
original: 32
new: 40
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
Example 1 cont
Find the percent using the original number, 32,
as the base.
percent change
change
100 percent
original amount
Find the cross products.
Simplify.
Divide each side by 32.
Simplify.
Answer: The percent of increase is 25%.
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
change
book store cost
percent change
100 percent
Find the cross products.
Distributive Property
Add 500 to each side.
Simplify.
Divide each side by 100.
Simplify.
Answer: The selling price of the $5 book is $6.40.
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
Discount A dog toy is on sale for
20% off the original price. If the
original price of the toy is $3.80,
what is the discounted price?
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.
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
amount of change
– The proportion ---------------------------original amount
=
r
------100
is used to find the percents of change (r)
• Homework:
– none