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 $ 3 n= 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 = 1470 49.00 – 14.70 = 34.30 N= 14.70 Sale 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 = 300 Shipping 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= interest 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+150= $2650 = 2500(3%)(2) =2500(.03)(2) =150

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%