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### Applications of Percents

- A percent of change is an increase or decrease expressed as a percent. If the new value is greater than the original one, it is a percent of increase; otherwise, it is a percent of decrease.
- Sales tax is a familiar example of a percent of increase.
- Discount is an example of a percent of decrease.
- When solving these kinds of problems, always write the percent as either a fraction with a denominator of 100 or a decimal equivalent to the percent.

### Applications of Percents

The temperature increases from thirty to sixty degrees. What is the percent of change?

- percentage change = [(final value − original value)/original value] ×100
- original temperature = 30

final temperature = 60 - percentage ∆ = frac60 − 3060 ×100
- percentage ∆ = frac3060 ×100
- percentage ∆ = 0.5 ×100 = 50

percentage ∆ = 50%

The temperature increases from sixty - two to seventy - five degrees. What is the percent of change?

- percentage change = [(final value − original value)/original value] ×100
- original temperature = 62 final temperature = 75
- percentage ∆ = [(75 − 62)/75] ×100
- percentage ∆ = [13/75] ×100
- percentage ∆ = [1300/75] = 17.―3

percentage ∆ ≈ 17.3%

A coat costs thirty - five dollars. The sales tax is seven percent. What is the total price?

- Price of coat + sales tax = total price
- sales tax = (.07)(35) = 2.45

35 + 2.45 = $37.45

A computer costs four hundred seventy - two dollars. The sales tax is eight percent. What is the total price?

- Price of computer + sales tax = total price
- sales tax = (.08)(472) = 37.76

472 + 37.76 = $ 509.76

A bicycle was originally priced at one hundred twelve dollars, but is discounted fifteen percent. What is the discounted price of the bicycle?

- Original price - amount of discount = final price

discount = (.15)(112) - 112 − (.15)(112) =
- 112 − 16.8 =

95.2

A dress was originally priced at sixty - nine dollars, but is discounted ten percent. How much is the dress now?

- Original price - amount of discount = final price

discount = (.10)(69) - 69 − (.10)(69) =
- 69 − 6.9 =

62.1

A suit was originally $160, but is discounted 30% . A sales tax of 7.5% is added, based on the discounted price.

What is the final price of the suit?

To the nearest percent, what is the percent of change between the original price and the final price paid, including sales tax?

What is the final price of the suit?

To the nearest percent, what is the percent of change between the original price and the final price paid, including sales tax?

- Original price - discount = discounted price

160 - (.30)(160) = discounted price - 160 − 48 = $ 112
- Discounted price + amount of sales tax = final price

112 + (.075)(112) = final price - 112 + 8.4 = $ 120.4
- percentage change = [(final value − original value)/original value] ×100
- [(120.4 − 160)/160] ×100
- [( − 39.6)/160] ×100
- − 0.2475 ×100 =

− 24.75

25% decrease

25% decrease

A camera was originally $225, but is discounted 15% . A sales tax of 7.5% is added, based on the discounted price.

What is the final price of the camera?

To the nearest percent, what is the percent of change between the original price and the final price paid, including sales tax?

What is the final price of the camera?

To the nearest percent, what is the percent of change between the original price and the final price paid, including sales tax?

- Original price - discount = discounted price

225 - (.15)(225) = discounted price - 225 - 33.75 = 191.25
- Discounted price + amount of sales tax = final price

191.25 + (.075)(191.25) = final price - 191.25 + 14.34 = $ 205.59
- percentage change = [(final value − original value)/original value] ×100
- [(205.59 − 225)/225] ×100
- [( − 19.41)/225] ×100

≈ −

**8****.****627****9****%**decreaseA chair costs $12. The sales tax is 8.25% . What is the total price?

- price of chair + sales tax = total price
- sales tax = (.0825)(12) = 0.99

12 + .99 = $12.99

A television costs $540 but is discounted 20% . What is the discounted price of the television?

- original price - amount of discount = final price
- discount = (.20)(540) = $108

540 − 108 = $ 432

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

### Applications of Percents

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro 0:00
- Definitions 0:15
- Percent of Increase
- Percent of Decrease
- Examples
- Sales Tax
- Discount
- Example 1: Temperature Change 3:12
- Example 2: Sales Tax 5:44
- Example 3: Clothing Discount 7:04
- Example 4: Sales and Discount 9:15

5 answers

Last reply by: Dr Carleen Eaton

Sat Aug 4, 2012 11:45 AM

Post by Thuc Pham on February 6, 2010

in ex:1, there was a mistake in the denominator where the final value was written instead of the original value