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Lesson 3-7 Percent of Change

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**Objectives Find the percents of increase and decrease**

Solve problems involving percents of change

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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.

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**Key Concepts Step 1: Explore the Problem Step 2: Plan the Solution**

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?

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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

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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. Divide each side by 32. Simplify. Answer: The percent of increase is 25%.

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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.

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**Example 2 cont Find the cross products. Distributive Property**

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.

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Example 3 Sales Tax A meal for two at a restaurant costs 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 $ to $1.64. Add this amount to the original price. Answer: The total price of the meal is $34.49.

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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.

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**Summary & Homework Summary: Homework:**

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

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