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**Ratio, Percent, Proportion**

Pg 16 Ratio, Percent, Proportion EQ: How do you use percentages to calculate tax, tip, commission, mark-ups, discounts and other real world contexts? OBJ: 1.01 Problem of the Day: Is the percent of decrease from 80 to 50 the same as the percent of increase from 50 to 80? Why? Or Why not?

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**Ratio, Percent, Proportion**

Pg 16 EQ: How do you use percentages to calculate tax, tip, commission, mark-ups, discounts and other real world contexts? OBJ: 1.01 Problem of the Day: Jon and Amie each purchased a pair of shoes during the annual sale at the Shoe Factory. All shoes were priced 40% off the original price. If Jon paid $35 for his shoes, what was the original price? If Aime bought a pair of shoes originally priced at $79, what was the sale price?

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**Vocabulary Tax: Additional cost which goes to the government**

Tip: Additional cost which goes to the service Commission: A form of payment for service Mark-up: Additional cost added by the manufacturer

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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. A. 65 is decreased to 38. Find the amount of change. 65 – 38 = 27 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. B. 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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Try This: Example 1A Find the percent of change. Round answers to the nearest tenth of a percent, if necessary. A. 70 is decreased to 45. Find the amount of change. 70 – 45 = 25 25 70 Substitute values into formula. percent of change = Divide. 35.7% Write as a percent. Round. The percent of decrease is about 35.7%.

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Try This: Example 1B Find the percent of change. Round answers to the nearest tenth of a percent, if necessary. B. 37 is increased to 56. 56 – 37 = 19 Find the amount of change. 37 19 Substitute values into formula. Percent of change = Divide. 51.4% Write as a percent. Round. The percent of increase is about 51.4%

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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 2A & 2B: Using Percent of Change**

The regular price of a bicycle helmet is $ It is on sale for 20% off. A. Find the actual amount of the discount. 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 discount is $8.60. B. Find the sale price. Subtract the discount from the regular price. $42.99 – $8.60 = $34.39 The sale price is $34.39

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**A. Find the actual amount of the discount.**

Try This: Example 2A & 2B The regular price of a computer game is $ It is on sale for 15% off. A. Find the actual amount of the discount. 15% · = d Think: 15% of $49.88 is what number? 0.15 · = d Write the percent as a decimal. 7.482 = d Multiply. $7.48 d Round to the nearest cent. The discount is $7.48. B. Find the sale price. Subtract the discount from the regular price. $49.88 – $7.48 = $42.40 The sale price is $42.40

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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 selling price of the T-shirts? First 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. The amount of increase is $ Now find the selling price. Think: retail price = wholesale price + amount of increase. p = $ $13.86 p = $26.46 The retail price of the hand-painted T-shirts is $26.46 each.

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**Insert Lesson Title Here**

Try This: Example 3 William makes T-shirts for $7.00 each and sells them after a price increase of 125%. What is the selling price of the T-shirts? First find the actual amount of increase. Think: 125% of $7.00 is what number? 125% · 7.00 = n 1.25 · 7.00 = n Write the percent as a decimal. 8.75 = n Multiply. The amount of increase is $8.75. Now find the selling price. Think: retail price = wholesale price + amount of increase. r = $ $8.75 r = $15.75 The retail price of the T-shirts is $15.75 each.

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**Insert Lesson Title Here**

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. is decreased to 90. 5. A backpack that sells for $42 is on sale for % off. Find the amount of discount and the sale price. 20% 80% 90% 25% $10.50, $31.50

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