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?

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?

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

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 =

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 =  0.4153846 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

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 =  1.2439 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

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 =  0.35714 Divide.  35.7% Write as a percent. Round. The percent of decrease is about 35.7%.

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 =  0.51351 Divide.  51.4% Write as a percent. Round. The percent of increase is about 51.4%

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

Additional Example 2A & 2B: Using Percent of Change The regular price of a bicycle helmet is $42.99. It is on sale for 20% off. A. Find the actual amount of the discount. 20% · 42.99 = d Think: 20% of $42.99 is what number? 0.20 · 42.99 = 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

A. Find the actual amount of the discount. Try This: Example 2A & 2B The regular price of a computer game is $49.88. It is on sale for 15% off. A. Find the actual amount of the discount. 15% · 49.88 = d Think: 15% of $49.88 is what number? 0.15 · 49.88 = 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

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% · 12.60 = n 1.10 · 12.60 = n Write the percent as a decimal. 13.86 = n Multiply. The amount of increase is $13.86. Now find the selling price. Think: retail price = wholesale price + amount of increase. p = $12.60 + $13.86 p = $26.46 The retail price of the hand-painted T-shirts is $26.46 each.

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 = $7.00 + $8.75 r = $15.75 The retail price of the T-shirts is $15.75 each.

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. 4. 120 is decreased to 90. 5. A backpack that sells for $42 is on sale for 25% off. Find the amount of discount and the sale price. 20% 80% 90% 25% $10.50, $31.50