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Percent. Applications of Proportional Relationships . TLW use proportions to find taxes and gratuities, markups and markdowns on items for sale, commission and fees, simple interest, percent increase or decrease, and percent error. . Proportion .

Percent

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Percent

Applications of Proportional Relationships

• TLW use proportions to find taxes and gratuities, markups and markdowns on items for sale, commission and fees, simple interest, percent increase or decrease, and percent error.

Proportion

• Proportions can be used to solve problems involving percents. The following proportion can be used to find an unknown value.

Sales Tax and Gratuities

• Percents are often used when describing and solving problems involving sales tax and gratuities.

• The sales tax rate varies by state, and sometimes by city. It is a percent of the total cost of items purchased.

Sales Tax Example

• Larry bought a video console for \$129. The sales tax in the state is 6%. How much tax did Larry pay for the video game console?

• Set up a proportion , and then cross multiply. Let n represent the amount of sales tax .

100(n) = 129(6) Larry paid \$7.74 in sales tax

100n = 774

N = 7.74

Gratuity

• A gratuity is a tip, or bonus, that is given for services that have been provided. It is usually computed as a percent of the total cost for a service.

Gratuity Example

Kyle’s family went out to dinner. The total for the bill was \$45. Kyle’s dad left a 15% tip. What was the amount of the tip?

Set up a proportion

100n = 675

N = 6.75

Tip was \$6.75

Markups

• A markup is the difference between the cost of an item and its selling price.

• If you know the cost of an item and the markup, you can find the selling price.

• Selling price = cost + markup

Markup Example

• A store buys sweatshirts for \$ 12 each and the marks up the price by 25%. What is the price of the sweatshirt at this store?

• Set up a proportion

100n = 300

Mark up is \$ 3n= 3

Total cost is 12 + 3 = \$15

Markdowns

• A markdown is the amount of an item reduced from its regular price.

• If you know the original price and the markdown, you can find the sale price.

• Sale price = original price – markdown

Markdown Example

• The original price of a pair of shoes was \$49. The price of the shoes are marked down 30%. What is the sale price of the shoes?

• Set up proportion

• n⁄49 = 30⁄100

• 100n = 147049.00 – 14.70 = 34.30

• N= 14.70Sale price is: \$ 34.30

• Markdown is \$14.70

Commissions and Fees

• A commission is an amount of money paid to a salesperson based on his or her total amount of sales and the commission rate.

• A fee is an amount added to the cost of an item for service.

Commission Example

• Richard is paid 8% commission on his carpet sales. How much commission will Richard earn for sales of \$1650?

• Set up proportion

• n⁄1650 = 8⁄100

• 100n = 13,200

• N= 132

• Richard will earn \$132 in commission

Fee Example

• Mindy bought a gift online for \$15. This included a shipping fee of \$3. What percent of the cost of the gift was the shipping fee?

• Set up proportion

• 3⁄15 = n⁄100

• 15n = 300Shipping fee was 20%

• N =20

• 20/100 = 20%

Interest Rate

• Interest is the amount you are charged when you borrow money or the amount you are paid when you invest money.

• The principal is the original amount invested or borrowed.

• The interest rate is a percent of the principal.

Simple Interest

• Simple interest is paid only on the principal and is paid at the end of an investment time period.

• TO FIND SIMPLE INTEREST USE THE FORMULA:

I = prt

I= amount of Interest

P= principal

R= interst rate

T= time in years

Simple interest rate example

• Tom borrowed \$ 300 to buy a mountain bike. If he pays interest at a rate of 4% on a 6-month loan, how much interest will he pay?

• I=prt

• 300 ( 4%) ( ½)

• 300(.04)(.5)

• = 6

• Tom will pay \$6 interest on his loan

Simple interest example # 2

• Vic deposited \$2500 into a savings account that pays her simple interest. The interest rate is 3%. How much interest will Vic earn in 2 years? What will Vic’s account balance be after 2 years?

• I=prt

• = 2500(3%)(2)

• =2500(.03)(2)

• =150

• 2500+150= \$2650

Percent of Increase or Decrease

• The percent of increase or decrease is the change from a given amount expressed as a percent of that amount.

• To find the percent of increase use the following proportion:

• New amount- original amount/ original amount =n/100

• To find the percent of decrease use the following proportion:

• Original amount – new amount / original amount =n/100

Percent of Increase Example

• In one year, Braden’s height went from 60 inches to 63 inches. What was the percent of increase in his height?

• New amount- original amount/ original amount =n/100

63-60/60 = n/100

3/60 =n/100

300 = 60n

N=5

5/100 = 5%

His height increased 5% in one year.

Percent of decrease Example

• Tara purchased a DVD player for \$150. Six months , the same DVD player was selling \$120. What was the percent of decrease on the price?

• Original amount – new amount / original amount =n/100

• 150-120/150 = n/100

• 30/150 = n/100

• 3000=150n 20=n

• 20/100= 20%

• DVD player decreased by 20%