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Warm UpSolve.
1. 10% of what number is 6?
2. What percent of 20 is 8?
3. What is 80% of 60?
4. 50 is what percent of 200?
60
40%
48
Course 2
6-6 Percent of Change
25%
Wednesday February 1, 2012
Homework pg. 354 #7-182/01/12
Learn to solve problems involving percent of change.
7.RP.2a-1 - Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table.
EQ Give an example in which the amount of
increase is greater than the original amount. What do you know about the percent?
Course 2
6-6 Percent of Change
Vocabulary
percent of changepercent of increasepercent of decrease
Insert Lesson Title Here
Course 2
6-6 Percent of Change
Course 2
6-6 Percent of Change
A percent can be used to describe an amount of change. The percent of change is the amount, stated as a percent, that a number increases or decreases. If the amount goes up, it is a percent of increase. If the amount goes down, it is a percent of decrease.
You can find the percent of change by using the following formula.
Percent of change = amount of changeoriginal amount
Find the percent of change. Round answers to the nearest tenth of a percent, if necessary.
Additional Example 1A: Finding Percent of Change
Course 2
6-6 Percent of Change
65 is decreased to 38.65 – 38 = 27
percent of change = 2765
0.4153846
The percent of decrease is about 41.5%.
Find the amount of change.Substitute values into formula.Divide.
Write as a percent. Round.
When a number is decreased, subtract the new amount from the original amount to find the amount of change.
Helpful Hint
41.5%
Find the percent of change. Round answers to the nearest tenth of a percent, if necessary.
Additional Example 1B: Finding Percent of Change
Course 2
6-6 Percent of Change
41 is increased to 92.92 – 41 = 51
Percent of change =41
1.2439
The percent of increase is about 124.4%
Find the amount of change.
Substitute values into formula.Divide.
Write as a percent. Round. 124.4%
51
When a number is increased, subtract the original amount from the new amount.
Helpful Hint
Find the percent of change. Round answers to the nearest tenth of a percent, if necessary.
Check It Out: Example 1A: pg. 155 #1
Course 2
6-6 Percent of Change
70 is decreased to 45.
70 – 45 = 25
percent of change = 2570
0.35714
The percent of decrease is about 35.7%.
Find the amount of change.
Substitute values into formula.
Divide.
Write as a percent. Round. 35.7%
Find the percent of change. Round answers to the nearest tenth of a percent, if necessary.
Check It Out: Example 1B: Work it in try this #1
Course 2
6-6 Percent of Change
37 is increased to 56.
56 – 37 = 19
Percent of change =37
0.51351
The percent of increase is about 51.4%
Find the amount of change.
Substitute values into formula.
Divide.
Write as a percent. Round. 51.4%
19
Course 2
6-6 Percent of Change
When you know the percent of change, you can use an equation to find the actual amount of change.
The regular price of a bicycle helmet is $42.99. It is on sale for 20% off. What is the sales price?
Additional Example 2: Using Percent of Change
Course 2
6-6 Percent of Change
Step 1: Find the actual amount of the discount.
20% · 42.99 = d
0.20 · 42.99 = d
8.598 = d
$8.60 d
The amount of the discount is $8.60.
Think: 20% of $42.99 is what number?
Write the percent as a decimal.
Multiply.
Round to the nearest cent.
The regular price of a bicycle helmet is $42.99. It is on sale for 20% off. What is the sales price?
Additional Example 2 Continued
Course 2
6-6 Percent of Change
Step 2: Find the sale price.
regular price – amount of discount = sales price
The sale price is $34.39
$42.99 – $8.60 = $34.39
The regular price of a computer game is $49.88. It is on sale for 15% off. What is the sales price?
Check It Out: Example 2: Pg. 155 # 2
Course 2
6-6 Percent of Change
Step 1: Find the actual amount of the discount.
15% · 49.88 = d
0.15 · 49.88 = d
7.482 = d
$7.48 d
The amount of the discount is $7.48.
Think: 15% of $49.88 is what number?
Write the percent as a decimal.
Multiply.
Round to the nearest cent.
Check It Out: Example 2 Continued
Course 2
6-6 Percent of Change
Step 2: Find the sale price.
regular price – amount of discount = sales price
The sale price is $42.40.
$49.88 – $7.48 = $42.40
The regular price of a computer game is $49.88. It is on sale for 15% off. What is the sales price?
A boutique buys hand-painted T-shirts for $12.60 each and sells them at a 110% increase in price. What is the retail price of the T-shirts?
Additional Example 3: Business Application
Course 2
6-6 Percent of Change
Step 1: Find the actual amount of increase.Think: 110% of $12.60 is what number?110% · 12.60 = n
1.10 · 12.60 = n
13.86 = n
Step 2: Find the selling price.
wholesale price + amount of increase = retail price
$12.60 + $13.86 = $26.46
The retail price of the hand-painted T-shirts is $26.46 each.
Write the percent as a decimal.
Multiply.
Check It Out: Example 3: pg 155 try this 3
Insert Lesson Title Here
Course 2
6-6 Percent of Change
William makes T-shirts for $7.00 each and sells them after a price increase of 125%. What is the retail price of the T-shirts?Step 1: Find the actual amount of increase.
Think: 125% of $7.00 is what number?
125% · 7.00 = n
1.25 · 7.00 = n
8.75 = n
Step 2: Find the selling price.
The retail price of the T-shirts is $15.75 each.
Write the percent as a decimal.
Multiply.
wholesale price + amount of increase = retail price
$7.00 + $8.75 = $15.75
Lesson Quiz
Find each percent of change.1. 10 is increased to 12.
2. 25 is increased to 45.
3. 10 is decreased to 1.
4. The regular price of a coat is $120. It is on sale for 25% off. What is the sale price?
5. A backpack that sells for $42 is on sale for 25% off. Find the sale price.
80%
20%
Insert Lesson Title Here
90%
$90
Course 2
6-6 Percent of Change
$31.50
Learn to solve problems involving percent of change.
7.RP.2a-1 - Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table.
EQ Give an example in which the amount of
increase is greater than the original amount. What do you know about the percent?
Course 2
6-6 Percent of Change
