4-5: Percent of Change

1. not edited yet 4-5: Percent of Change OBJECTIVES: You must solve problems involving percent of increase or decrease and those involving discounts or sales tax. • Initial Terms: • percent of decrease - percent a value has gone down by • If you had 100 pieces of candy on Monday and only twenty left on Tuesday, then you had an 80% decrease in your candy supply. (100 - 20)  100 then turn into a percent • percent of increase - percent a value has gone up by • This is essentially the same thing as the decrease - only it goes up.

2. amount of decrease 39 = original number 64 not edited yet 4-5: Percent of Change EXAMPLE 1: In 1982, the population of the California condor had dwindled to a total of 21, making it the rarest bird in North America. According to the Refuge Department of the U.S. Fish and Wildlife Service, however, there are 64 condors in existence in 1992 and 103 as of October 1995. Find the percent of increase in the population of California Condors from 1992 to 1995. METHOD 1 METHOD 2 First, subtract to find the amount of change. First, divide the new amount by the original amount. 103  64 = 1.609375 103 - 64 = 39 Then set up a proportion. Then subtract 1 from the result. 1.609375 - 1 = 0.609375 Finally, turn the decimal into a percent. 0.609375 60.9375%  61% Finally, solve it. r = 60.9375%  61%

3. not edited yet 4-5: Percent of Change EXAMPLE 1: Ayita received a coupon in the mail offering her a 20% discount on the price of a pair of jeans at Jean Express. Ayita visited the store and found a pair of jeans she wants to buy that cost $48. What will be the discounted price? (1) Explore: The original price is $48.00 and the discount is 20%. This means the price was DECREASED by 20%. (2) Plan: You want to find the amount of discount, then subtract that amount from $48.00. The result is the discounted price. (3) Solve: 20% of $48 = 0.20(48.00) = 9.60 Subtract this amount from the original price. $48 - $9.60 = $38.40 The discounted price is $38.40 (4) Examine: Does the discounted price seem reasonable? YES Another way to do this problem follows: (CPM) If the jeans are 20% off, then that means they must be 80% on. 80% on of $48 = 0.80(48) = $38.40 This is the way I calculate prices while shopping.

4. not edited yet 4-5: Percent of Change EXAMPLE 3: Katie Danko, a sophomore at Westerville North High School, is ordering a class ring. The ring she has chosen costs $169.99. She also needs to pay a sales tax of 53/4%. What is the total price? Another way to do this problem follows: (CPM) If the sales tax is 5.75%, the total price will be 100% plus the 5.75% = 105.75%. Take the original price times 105.75%: $169.99 * 105.75% = 169.99(1.0575) = $179.77 (1) Explore: The price is $169.99, and the tax rate is 53/4%. This means the price is increase by 53/4%. (2) Plan: First, find 53/4% of $169.99. Then add the result to $169.99. (3) Solve: 53/4% of $169.99 = 0.0575(169.99) = 9.774425  9.77 Add this to the original price: $169.99 + $9.77 = $179.77 (4) Examine: Does the discounted price seem reasonable? YES Therefore, the price including tax would be $179.77

5. not edited yet 4-5: Percent of Change HOMEWORK Page 225 #13 - 29 odd