# Percents What is a percent Percents are ratios

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Percents

What is a percent? Percents are…. ratios that compare a number out of 100 How to find a Percent: Percent ______ 100 = Part ______ Whole

Can you find the percent? 1. What percent of 92 is 66? (Round to the nearest whole) Step 1: Set up a proportion x 66 ______ = 100 92 Step 2: Cross Multiply 92 x = 100(66)

Can you find the percent? Step 3: Solve for your variable 92 x = 100(66) x = 71. 739 72% 66 is 72% of 92!

More Examples… 2. Emma walks 2 miles to school. If Rachel’s walk is 80% of the length of Emma’s walk, find the length of Rachel’s walk. 80 x _____ = 100 2 Rachel walked 1. 6 miles!

More Examples… 3. A jacket is on sale for 60% off its original price. The original price was \$30. What is the sale price? 60 x _____ = 100 30 The sale price was \$18!

More Examples… 4. Jon earns \$36, 000 yearly. Of that he pays \$12, 240 for his mortgage. What percent of his earnings goes to the mortgage? x 12240 _____ = 100 36000 34% of his earnings goes to the mortgage!

Percent Increase & Decrease Percent Change: The ratio comparing the amount change to the original amount. percent change = amount of change original amount Percent Increase: Describes how much the original amount increases. Percent Decrease: Describes how much the original amount decreases.

Examples… 1. According to the US Census, 72. 3 million children lived in the United States in 2004. It is estimated that there will be 80. 3 million children in 2020. What is the percent increase, to the nearest percent? 80. 3 million - 72. 3 million = 8 percent change = 8 72. 3 Percent Change = 0. 1106 11%

More Examples… 2. Anthony buys a LCD monitor for his new computer. The price tag says the original price is \$750 but it’s on sale for \$487. 50. What is the percent decrease? \$750. 00 - \$487. 50 = \$262. 50 percent change = 262. 50 750. 00 Percent Change = 0. 35 The LCD monitor was 35% off!

More Examples… 3. Ms. Breier bought a house for \$125, 000. It has increased in value by 7% in the past two years. Mr. Frommann bought a house for \$135, 000. His house decreased in value by 4%. Who’s house is currently worth more? Ms. Breier: 7 x ___ = 100 125000 x = 8750 \$125000 – \$8750 = \$116250 Mr. Frommann: 4 x ___ = 100 135000 x = 5400 \$135000 - \$54000 = \$129600

More Examples… 4. You see a house for sale down the road from you. The house is listed for \$294, 600. You are very interested and decide to put an offer down. You offer \$287, 000 for the home. What is the percent decrease of the offer to the listing price? \$294, 600 - \$287, 000 = \$7600 percent change = 7600 294600 Percent Change = 0. 0257 2. 6% Decrease!

Commission A fee paid to a person who makes a sale. ** Its is usually a percent of the selling price. Commission Rate: The percent of the sale. commission rate sales = commission

Examples… 1. Julie is paid a monthly salary of \$2, 100 plus commissions. Last month she sold one care for \$39, 500, earning a 4% commission on the sale. How much was her commission? What was her total pay for the month? 0. 04 \$39, 500 = commission Commission: \$1, 580 Monthly Pay: \$3, 680

Examples 2. A furniture sales associate earned \$960 in commission in May. If his commission is 12% of his sales, how much were his sales in May? 0. 12 sales = \$960 x = \$81, 000 He had \$81, 000 worth of sales in May.

Examples… 3. The realtor you hired in order to buy your home made \$6, 796 in commission. You bought your home for \$169, 900. What was the realtor’s commission rate? commission rate \$169, 900 = \$6, 796 x =. 04 The commission rate is 4%!

Sales Tax Sales tax is the tax on the sale of an item or service. ** Sales tax needs to be rounded to the nearest penny! Sales tax rate price = sales tax

Examples… 1. I bought a pair of jeans at the store. They were \$39. 99. I had to pay 8. 75% sales tax. How much did I have to pay in sales tax? 0. 0875 \$39. 99 = sales tax Sales Tax: \$3. 50 How much were the jeans with the sales tax? \$39. 99 + \$3. 50 = \$43. 49 I spent \$43. 49 total!

Examples… 2. If the sales tax rate is 7. 75%, how much sales tax would Michael have to pay in sales tax if he bought a portable DVD player for \$59. 99 and two DVD’s for \$17. 99 each? 0. 0775 (\$59. 99+2(\$17. 99)) = sales tax Sales Tax: \$7. 44 What is the total amount the Michael owes? \$95. 97 + \$7. 44 = \$103. 41

Examples… 3. Explain whether adding 6% sales tax to a total gives you the same result as finding 106% of the total. *Let’s use an example! -Say our total is \$20. 50 0. 06 \$20. 50 = sales tax Sales Tax: \$1. 23 \$20. 50 + \$1. 23 = \$21. 73 What is 106% of \$20. 50? 1. 06 \$20. 50 = sale price Sale Price: \$21. 73 They’re the same!

Examples… 4. Explain how to find the price of an item if you know the total cost after 5% sales tax. Let x = the price of your item Let 0. 5 x = the sales tax x + 0. 5 x = total cost

Examples… 5. Explain whether the sales tax on a \$20 item would be double the sales tax on a \$10 item. Justify your answer. *Lets use an example! -Say our sales tax is 8. 75%. 0. 0875 \$20 = sales tax Sales Tax: \$1. 75 0. 0875 \$10 = sales tax Tax: \$0. 88 (rounded) Sales \$1. 75/2 = \$0. 875

Examples… 6. You just bought your first home at a sale price for \$249, 500. New York state sales tax is 8. 75%. How much did he pay in sales tax? 0. 0875 \$249, 500 = sales tax Sales Tax: \$21, 831. 25 How much did you pay for your home total? \$249, 500 + \$21, 831. 25 = \$271, 331. 25

Simple Interest is money paid to the bank when you borrow the bank’s money OR it is money paid to you when you deposit money into a savings account. Simple Interest is a type of interest paid for the use of money. Simple Interest I=P Rate of interest is the percent charged or earned r Principal is the amount of money borrowed or invested t Time that the money is borrowed or invested (in years)

Examples… 1. Tristan borrowed \$14, 500 from his brother and promised to pay him back over 5 years at an annual simple interest rate of 7%. How much interest will he pay if he pays off the entire loan at the end of the fifth year? I = 14, 500 0. 07 5 I = \$5, 075 What is the total amount he will repay? \$14, 500 + \$5, 075 = \$19, 575

Examples… 2. Jamie invested \$3, 500 in a mutual fund at a yearly rate of 6%. He earned \$945 interest. For how long was the money invested. 945 = 3, 500 t 0. 06 4. 5 = t The money was invested for 4. 5 years!

Examples… 3. You are in the process of buying a home. You take out a mortgage loan for the sale price (including sales tax) of your house, which is \$309, 938. Since you are a first time home owner and plan on living in the house for the next 20 years, you will get a mortgage rate of 4. 5%. How much interest will you pay on the entire loan? I = 309, 938 0. 045 20 I = 278, 944. 2 You will pay \$278, 944 in interest!

#3 Continued… What will your monthly mortgage be, including interest? \$309, 938 + \$278, 944 = \$588, 882 - There are 12 months in a year, so how many months are in 20 years? 20(12) = 240 months \$588, 882 / 240 months Your monthly mortgage payment will be \$2, 453. 68!