Bell Ringer 11-7 ( Do in notebook) 5 minutes 1. Express 20% as a fraction in lowest terms and as a decimal Express 134% as a decimal. Express 6.5% as a decimal. Express 6.5% as a decimal. 4. Solve What is percent of change? What is percent of change? 5.

2.7 Percent of Change Objectives: By the end of the next class, with an 80% accuracy, students will be able to: Find the percents of increase and decrease by writing and solving proportions Find the percents of increase and decrease by writing and solving proportions Solve problems involving sales taxes and discounts Solve problems involving sales taxes and discounts

Key Terms Percent of change Percent of change Percent of increase Percent of increase Percent of decrease Percent of decrease Sales tax Sales tax Discount Discount Final price Final price

When an increase or decrease is written as percent, the percent is called percent of change. Percent of change is the ratio of the change to the original amount expressed as a percent. If the new number is greater than the original number, then the percent of change is a percent of increase. If the new number is lower than the original number, then the percent of change is a percent of decrease.

Step 1: Find the amount of change Step 2: Find the percent using the amount of change as the numerator and the original number as the denominator Step 3: Set up and solve a proportion to find the percent of increase or decrease. Ex. 1 Original: 25 New: 28 Step 1: 28 – 25 = 3 (increase) Step 2 and 3: change 3 = r original amount ( r) = 3(100) Cross products 25r = 300 Simplify Divide 25 on both sides r = 12 Simplify The percent of increase is 12%. FIND THE PERCENT OF CHANGE

Example 2: Original: 30 New: 12 Step 1: 30 – 12 = 18 (decrease) Step 2 and 3: change 18 = r original amount ( r) = 18(100) Cross Products 30r = 1800 Simplify Divide 30 on each side r = 60 Simplify The percent of decrease is 60%. FIND THE PERCENT OF CHANGE

p Shared Practice Do 1, 2, 17 and 19 Percent of change can be applied to sales tax and discounts. Sales tax is a tax that is added to the cost of an item. Is sales tax an example of a percent of increase or a percent of decrease? Sales tax is an example of a percent of increase. Discount is the amount by which the regular price of an item is reduced. Is discount an example of a percent of increase or a percent of decrease? Discount is an example of a percent of decrease.

Software costs $ Sales tax is 6.5%. Find the total price of the item. The tax is 6.5% of the cost of the software. Change 6.5% to a decimal (move decimal 2 places left) = % of $39.50 =.065 ($39.50) = $ Round $ to $2.57 (tax). Add this amount (tax) to the original price $ $2.57 = $42.07 The total price is $ FIND THE AMOUNT AFTER SALES TAX

P. 121 #6 dress: $22.50; sales tax 7.5% The tax is 7.5% of the cost of the software. Change 7.5% to a decimal (move decimal 2 places left) = % of $22.50 =.075 ($22.50) = $ Round $ to $1.69 (tax). Add this amount (tax) to the original price $ $1.69 = $24.19 The total price is $24.19.

8. Prom: A limo costs $85 to rent 3 hours plus a 7% sales tax. What is the total cost to rent the limo for 6 hours? 8. Prom: A limo costs $85 to rent 3 hours plus a 7% sales tax. What is the total cost to rent the limo for 6 hours?

HW p even, 24, 26 Bring an ad from the sales paper of an item showing work finding the percent of increase. EXIT SLIP p and 4

p.163 #10. A pair of jeans is on sale for 25% off. The cost of the jeans is $45. Find the discounted price of the jeans. The discount is 25% off the original price. Step 1: 25% of 45 =.25 (45) = $11.25 (amount of discount) Step 2: Subtract $11.25 from the original price. $45 - $11.25 = $33.75 (discounted price) The cost of the jeans after the discount is $ FIND THE AMOUNT AFTER A DISCOUNT

FINDING THE FINAL PRICE # 43. A lamp is $120. It is on sale for 20% off and there is a 6% sales tax on the lamp. Find the final price of the lamp. Step 1: Find the discounted price..20 (120) = $24 Step 2: Subtract the discount amount from the price of lamp $120 – $24 = $96 Step 3: Find the amount of the sales tax..06 (96) = 5.76 (amount of sales tax) Step 4: Find the final price (amount after sales tax is included. $96 + $5.76 = $ The final price of the lamp is $