© William James Calhoun, 2001

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 byIf 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 byThis is essentially the same thing as the decrease - only it goes up.

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© William James Calhoun, 2001

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.

103 - 64 = 39Then set up a proportion.

amount of decrease 39

original number 64=

100

r

64

39

Finally, solve it.r = 60.9375% 61%

First, divide the new amount by the original amount. 103 64 = 1.609375Then subtract 1 from the result.

1.609375 - 1 = 0.609375Finally, turn the decimal into a percent.

0.609375 60.9375% 61%

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© William James Calhoun, 2001

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) = $38.40This is the way I calculate prices while shopping.

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© William James Calhoun, 2001

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?

(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?

YESTherefore, the price including tax would be $179.77

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

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© William James Calhoun, 2001

4-5: Percent of Change

HOMEWORK

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