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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 .

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Percent

Percent


Applications of proportional relationships

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

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

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

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

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

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

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

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

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

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

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

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

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 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

  • 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

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

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

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 i ncrease e xample

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

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%


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