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Notes 29 Percent of Change 6-4

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Vocabulary Percent of change- the amount, stated as a percent, that a number increases or decreases. Percent of increase- when the amount of change goes up. Percent of decrease- when the amount of change goes down.

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**A percent can be used to describe an amount 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. amount of change original amount Percent of change =

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**Additional Example 1A: Finding Percent of Change**

Find the percent of change. Round answers to the nearest tenth of a percent, if necessary. 65 is decreased to 38. 65 – 38 = 27 Find the amount of change. 27 65 Substitute values into formula. percent of change = Divide. 41.5% Write as a percent. Round. The percent of decrease is about 41.5%. When a number is decreased, subtract the new amount from the original amount to find the amount of change. Helpful Hint

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**Additional Example 1B: Finding Percent of Change**

Find the percent of change. Round answers to the nearest tenth of a percent, if necessary. 41 is increased to 92. 92 – 41 = 51 Find the amount of change. 41 51 Substitute values into formula. Percent of change = Divide. 124.4% Write as a percent. Round. The percent of increase is about 124.4% When a number is increased, subtract the original amount from the new amount. Helpful Hint

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Check It Out: Example 1A Find the percent of change. Round answers to the nearest tenth of a percent, if necessary. 70 is decreased to 45.

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Check It Out: Example 1B Find the percent of change. Round answers to the nearest tenth of a percent, if necessary. 37 is increased to 56.

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**When you know the percent of change, you can use an equation to find the actual amount of change.**

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**Additional Example 2: Using Percent of Change**

The regular price of a bicycle helmet is $ It is on sale for 20% off. What is the sales price? Step 1: Find the amount of the discount d. 20% · = d Think: 20% of $42.99 is what number? 0.20 · = d Write the percent as a decimal. 8.598 = d Multiply. $8.60 d Round to the nearest cent. The amount of the discount is $8.60.

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**Additional Example 2 Continued**

The regular price of a bicycle helmet is $ It is on sale for 20% off. What is the sales price? Step 2: Find the sale price. regular price – amount of discount = sales price $ – $ = $34.39 The sale price is $34.39

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Check It Out: Example 2 The regular price of a computer game is $ It is on sale for 15% off. What is the sales price?

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**Additional Example 3: Business Application**

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? Step 1: Find the actual amount of increase. Think: 110% of $12.60 is what number? 110% · = n 1.10 · = n Write the percent as a decimal. 13.86 = n Multiply. Step 2: Find the selling price. wholesale price + amount of increase = retail price $ $ = $26.46 The retail price of the hand-painted T-shirts is $26.46 each.

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Check It Out: Example 3 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?

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