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Percents

Percents. What is a percent?. Percents are…. ratios that compare a number out of 100 How to find a Percent: ______ ______. Percent. Part. =. 100. Whole. Can you find the percent?. What percent of 92 is 66? (Round to the nearest whole) Step 1: Set up a proportion

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Percents

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  1. Percents

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

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

  4. Can you find the percent? Step 3: Solve for your variable 92x = 100(66) x = 71.739 72% 66 is 72% of 92!

  5. 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. _____ _____ Rachel walked 1.6 miles! 80 x = 100 2

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

  7. 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? _____ _____ 34% of his earnings goes to the mortgage! x 12240 = 100 36000

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

  9. 8 72.3 percent change = Examples… • 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 = 0.1106 11%

  10. 262.50 750.00 percent change = 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 = 0.35 The LCD monitor was 35% off!

  11. 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: Mr. Frommann: ___ ___ ___ ___ x = 8750 x = 5400 $125000 – $8750 = $116250 $135000 - $54000 = $129600 7 x 4 x = = 100 125000 100 135000

  12. 7600 294600 percent change = 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 = 0.0257 2.6% Decrease!

  13. 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

  14. Examples… • 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? Commission: $1,580 Monthly Pay: $3,680 0.04$39,500 = commission

  15. 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? x = $81,000 He had $81,000 worth of sales in May. 0.12sales = $960

  16. 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? x = .04 The commission rate is 4%! commission rate$169,900 = $6,796

  17. 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

  18. Examples… • 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? Sales Tax: $3.50 How much were the jeans with the sales tax? $39.99 + $3.50 = $43.49 I spent $43.49 total! 0.0875$39.99 = sales tax

  19. 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? Sales Tax: $7.44 What is the total amount the Michael owes? $95.97 + $7.44 = $103.41 0.0775 ($59.99+2($17.99)) = sales tax

  20. 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 Sales Tax: $1.23 $20.50 + $1.23 = $21.73 What is 106% of $20.50? Sale Price: $21.73 0.06$20.50 = sales tax They’re the same! 1.06$20.50 = sale price

  21. 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 0.5x = the sales tax x + 0.5x = total cost

  22. 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%. Sales Tax: $1.75 Sales Tax: $0.88 (rounded) $1.75/2 = $0.875 0.0875$20 = sales tax 0.0875$10 = sales tax

  23. 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? Sales Tax: $21,831.25 How much did you pay for your home total? $249,500 + $21,831.25 = $271,331.25 0.0875$249,500 = sales tax

  24. Rate of interest is the percent charged or earned Simple Interest Time that the money is borrowed or invested (in years) Principal is the amount of money borrowed or invested I= Prt Simple Interest 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.

  25. Examples… • 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 = $5,075 What is the total amount he will repay? $14,500 + $5,075 = $19,575 I = 14,500  0.07  5

  26. 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. 4.5 = t The money was invested for 4.5 years! 945 = 3,500  0.06  t

  27. 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 = 278,944.2 You will pay $278,944 in interest! I = 309,938  0.045  20

  28. #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!

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