Free Pre-Algebra Lesson 42 ! page 1 Lesson 42 A Few Consumer Percents Some of the most common uses of percents involve money. Sales Tax Most governments raise their operating costs through taxes. One form of tax commonly imposed by state and local governments in the U.S. is the sales tax. When an item is sold in a particular state, the state government collects a tax of some percent of the sale price. (Sometimes there is an additional county, district, or city sales tax as well.) When you buy an item, the price charged by the store is called the purchase price. Sales tax is added to the purchase price at the time you buy the item. If you pick up an item that has a price tag reading $4.99, you will have to pay the $4.99 plus some additional amount of sales tax at the register. Table of Sales Tax Rates, by State (January, 2010) Alabama 4.00% Alaska nil Arizona 5.60% Arkansas 6.00% California 8.25% Colorado 2.90% Connecticut 6.00% Delaware nil Florida 6.00% Georgia 4.00% Hawaii 4.00% Idaho 6.00% Illinois 6.25% Indiana 7.00% Iowa 6.00% Kansas 5.30% Kentucky 6.00% Louisiana 4.00% Maine 5.00% Maryland 6.00% Massachusetts 6.25% Michigan 6.00% Minnesota 6.88% Mississippi 7.00% Missouri 4.23% Montana nil Nebraska 5.50% Nevada 6.85% New Hampshire nil New Jersey 7.00% New Mexico 5.00% New York 4.00% North Carolina 5.75% North Dakota 5.00% Ohio 5.50% Oklahoma 4.50% Oregon nil Pennsylvania 6.00% Rhode Island 7.00% South Carolina South Dakota Tennessee Texas Utah Vermont Virginia West Virginia Wisconsin 6.00% 4.00% 7.00% 6.25% 4.70% 6.00% 5.00% 6.00% 5.00% Since the sales tax is a percent of the purchase price, the amount of tax you pay is proportional to the amount you spend. You pay more tax on expensive items than on cheaper items. The sales tax is a percent of the purchase price. amount = percent • base The amount of tax you pay is figured out as a part of the price, but then it is added to the price. For example, if the tax is 6%, you figure out 6% of the purchase price, then add it to the purchase price. The price you pay is 106% of the purchase price. + For example, with a sales tax of 6%, an item with a purchase price $1.00 will have a tax of $0.06 (6¢ is 6% of 100¢). This is why a 6% tax rate is sometimes described as “six cents on the dollar.” You pay $1.00 + $0.06 = $1.06. $1.00 goes to the store, and the $0.06 goes to the state government to pay for roads, schools, sewer lines, and other government services. © 2010 Cheryl Wilcox Free Pre-Algebra Lesson 42 ! page 2 Example: On your visit to West Virginia, you found a great guitar that you want to buy. The store is charging $1,250 for the guitar. What will the sales tax be? How much money do you need in all? Sales tax in West Virginia is 6%, according to the table on the previous page. The base is the purchase price. Sales tax = 6% of purchase price Sales tax = 0.06 • $1250 Sales tax = $75 You have to pay the $1250 purchase price, plus $75 in sales tax, for a total of $1250 + $75 = $1325 The total will be $1325. Example: Now that you’re back home in California, you feel you must buy an amplifier that is priced at $550. How much will you pay with tax included? Sales tax in California is 8.25%, according to the table on the previous page. You can either figure out the sales tax, then add it to the purchase price, OR you can find 108.25% of the purchase price. That’s 100% of the price, all of it, plus the 8.25% tax, all rolled up into one percent. Price including tax = 108.25% of purchase price Price including tax = 1.0825 • $550 Price including tax = $595.375 The price should be rounded to the nearest whole cent. Price including tax = $595.38 Leaving a Tip Eating in a restaurant in the U.S. usually involves leaving a tip for the wait staff. The standard amount for a restaurant tip is 15% to 20% of the cost of the meal. We’ll assume the cost of the meal is the price before any sales tax is added. The tip is a percent of the cost of the meal. amount = percent • base Like sales tax, a tip is figured out as part of the base price, but then it is added to the base price, becoming part of the total + cost of your meal. The cost of the meal plus 15% tip. + The cost of the meal plus 20% tip. + © 2010 Cheryl Wilcox + Free Pre-Algebra Lesson 42 ! page 3 Example: After enjoying their lovely anniversary dinner, Ashley and Clark must figure out the tip. The bill for the dinner before tax was $78.00. They decide to leave a 20% tip because the service was so great. How much should they leave? The tip is 20% of the cost of the meal. Tip = 0.2 • $78 = $15.60 20% of the cost of the meal is $15.60. Because a tip is a variable percentage between 15% and 20%, Clark and Ashley might round down to $15, since that amount will still be in the correct range. Example: Like many restaurants, Jack’s includes a 15% gratuity (tip) on the bill for parties with 6 or more people. The office lunch party at Jack’s had 8 people, and the bill came to $170. How much did the restaurant charge for the gratuity? The gratuity is 15% of the cost of the meal. Gratuity = 0.15 • $170 = $25.50 15% of the cost of the meal is $25.50. Since sales tax in California is 8.25%, if you double the sales tax you get 16.5%. Since 16.5% is between 15% and 20%, many Californians figure out a restaurant tip by doubling the sales tax amount. Example: Romelia had a salad and soft drink for a total of $11.99, and Hans had a burger and milkshake, which cost $15.89. They decided to tip double the sales tax of 8.25%. How much did they pay, including sales tax and tip? Romelia’s meal + Hans meal = combined cost of meal $11.99 + $15.89 = $27.88 Sales tax is 8.25% of $27.88 Sales tax = 0.825 • $27.88 = $2.3001 The sales tax will be $2.30 The tip is twice the sales tax. Tip is 2 • $2.30 = $4.60. They pay $27.88 + $2.30 + $4.60 = $34.78 Interest on Loans or Savings Another percent that is added to the base amount is the interest earned on savings or paid on a loan. Interest can be figured in quite complicated ways, but the basic idea is to add some percent of the base (the money saved or borrowed) to the base. Interest is like a fee charged for use of the money. If you keep your money in the bank, they use it and so pay you a fee, which is some percent interest. If you borrow money from the bank, they charge you a fee for your use of the money, again, some percent interest of the original loan. Interest is a percent of the money saved or borrowed. amount = percent • When doing interest calculations, the base is called the principal. © 2010 Cheryl Wilcox base (principal) Free Pre-Algebra Lesson 42 ! page 4 Example: At the beginning of the year, Harmony had $3,568.90 in her savings account, which earned 2% interest each year. She didn’t spend any of the money. After one year had passed, the bank added the interest to the account. How much interest did they add? How much money did Harmony have in the account after the interest was added? The interest is 2% of $3,568.90. interest = 0.02 • $3,568.90 interest = $71.378 rounded to the nearest cent, $71.38 Harmony had $3,568.90 + $71.38 = $3,640.28 Example: Sahira borrowed $5,200 to buy a car, and agreed to pay back the loan amount plus 12% interest within one year. How much did she pay back in all? Like the sales tax, you can either figure out 12% interest and add it to the loan, or find 112% of the loan, which will be the total amount to pay back. total repayment is 112% of loan amount = 1.12 • $5,200 = $5824 Sahira will end up paying back $5,824. Sale Prices The previous percents in this section were added on to the base. But a sale offers some percent off the original price, which is subtracted from that price to make a new, cheaper price. When calculating percents in a sale, the base is always the original price of the item. The sale price is 15% off the original price. The sale price is 40% off the original price. The whole square is the original price. The whole square is the original price. The white squares represent the 15% taken off the price. The 40% off is white. The green squares that remain are the new sale price. The new sale price is 100% – 40% = 60% of the original. The green squares left represent the new sale price. Notice that the green squares are 100% – 15% = 85% of the original price. After subtracting 40%, you pay 60% of the original price. There are two ways to find out how much you’re going to pay for an item on sale. Method 1: You can figure out the savings and subtract that from the original price to find what you will pay. Your savings are 40% of the original price. Original price – savings = Price you pay. © 2010 Cheryl Wilcox Free Pre-Algebra Lesson 42 ! page 5 Method 2: You can subtract the percent you save from 100% and use the result to calculate the price you pay. Your savings are 40% of the original price. 100% – 40% = 60% You pay 60% of the original price. You should use whichever method makes the most sense to you, or the one that is easiest for the situation. Example: That great leather jacket you’ve been wanting is finally on sale for 25% off. It originally cost $380. How much will you save? How much will it cost? You save 25% of $380. You save 0.25 • $380 = $95. 100% – 25% = 75% The cost is 75% of the original cost. The cost is 0.75 • $380 = $285. Note that $380 – $95 = $285. ! © 2010 Cheryl Wilcox Free Pre-Algebra Lesson 42 ! page 6a Lesson 42: A Few Consumer Percents Worksheet Name________________________________________ 1. Suppose you go to Illinois and buy 2 tickets to see the Bears in the playoffs. The tickets cost $450 each, and there is also a $17.50 processing fee per ticket. The state sales tax rate in Illinois is 6.25%, charged on the entire amount of the sale, including fees. How much will the total be? 2. In California, cities and counties may impose additional sales tax above the state tax. In Pleasant Hill, California, the total state and local sales tax is 9.25%. Find the sales tax you pay on a pair of shoes for $110 in Sun Valley mall in Pleasant Hill, California. 3. The dinner bill was $85.60. Figure a tip of 15% and one of 20% on the bill. 4. Juaquin borrowed $3000 at 8% interest. At the end of the year he must pay back the $3000 plus the interest. How much will he pay in all? 5. Shayla saved 25% on the bedlinens. The original price was $145. How much did she save? How much did she pay? 6. The jeans originally cost $85, but the sale was for 40% off. What was the sale price of the jeans? 7. “See this nifty hedgetrimmer? What a great sale! 60% off! I saved $54.” 8. Lindsey found the same Baby PlayZone that sells for $119.99 at the store for $20 at a garage sale. “How much was it originally?” The garage sale price is what percent of the store price? “How much did you spend?” What percent did Lindsey save? © 2010 Cheryl Wilcox Free Pre-Algebra Lesson 42 ! page 7 Lesson 42: A Few Consumer Percents Homework 42A 1. You are making a large sign to advertise the big prize in your club’s raffle – an iPod shuffle. The shuffle is 1.24 inches wide and 1.14 inches tall. If your picture will be 16 inches wide, how tall should it be to be similar to the real shuffle? Name________________________________________ 2. Revell 1:39 Wright Flyer "First Powered Flight" 1:39 Scale. Measures 6 3/4" in length and has a wingspan 12 1/4". December 17, 1903: Orville and Wilbur Wright made history one century ago on the sands of Kitty Hawk, NC, when they successfully flew the flying machine that they had built. What was the length and wingspan of the original Wright Brother’s flying machine, in feet? 3.Gasoline weighs 6.073 pounds per gallon. If you fill your gas tank with 30 gallons, how much does the gas weigh? 4. The average height of a man in the U.S. in 2010 was 5’10”. The average weight was 191 lbs. Find the average BMI for men in the U.S. based on the average height and weight. BMI = 703W lb (H in)2 5. If you travel 336 miles on your 30 gallons of gas, what is your gas mileage? 6. A house that costs $488,750 is 1,850 square feet. What is the price per square foot? 7. Fill in the table with the missing equivalents. 8. Fill in the table with the missing equivalents. FRACTION DECIMAL PERCENT FRACTION DECIMAL PERCENT 1/8 1% 1/4 2% 3/8 6.25% 1/2 9.75% 7/8 11.2% © 2010 Cheryl Wilcox Free Pre-Algebra Lesson 42 ! page 8 9. Leisha’s home is 1,625 square feet and she is using 450 square feet for her daycare business. To figure out her tax deduction she has to find the percent of her home’s square footage used by her business. 10. Shasha found that there were 1,483 songs on his iPod that he had only listened to once. His iPod held 9,447 songs. What percent of the songs had he listened to only once? 11. A ballot measure passed with 63% of the vote. If 276,801 people voted, how many voted in favor? 12. Drew Brees completed 68.1% of the 658 passes he attempted in 2010. How many passes did he complete? 13. You are buying a new car for $28,799. You can buy it in Sacramento, where the sales tax rate is 8.75% or in Walnut Creek, where the sales tax rate is 9.25%. How much will you save on sales tax if you buy the car in Sacramento? 14. Brittney was visiting her cousins in another state and thought the sales tax seemed low. She had bought a souvenir for $19.99 and the sales tax was $0.80. What was the sales tax rate? 15. The waiter was so funny and sweet that we decided to leave him a 20% tip. The meal cost $72.80. What was the tip? 16. The savings of $5230 will earn 1.8% interest this year. How much will the interest be? 17. A new copy of the textbook costs $162.67. If a used copy is 60% off the price of a new copy, what is the used textbook price? 18. For a limited time, you can save 30% on a gym membership. The usual price is $35 per month. What is the discounted price? © 2010 Cheryl Wilcox Free Pre-Algebra Lesson 42 ! page 9 Lesson 42: A Few Consumer Percents Homework 42A Answers 1. You are making a large sign to advertise the big prize in your club’s raffle – an iPod shuffle. The shuffle is 1.24 inches wide and 1.14 inches tall. If your picture will be 16 inches wide, how tall should it be to be similar to the real shuffle? W 1.24 16 = H 1.14 h 1.24h = 16 • 1.14 1.24h = 18.24 1.24h / 1.24 = 18.24 / 1.24 h ! 14.7 2. Revell 1:39 Wright Flyer "First Powered Flight" 1:39 Scale. Measures 6 3/4" in length and has a wingspan 12 1/4". December 17, 1903: Orville and Wilbur Wright made history one century ago on the sands of Kitty Hawk, NC, when they successfully flew the flying machine that they had built. What was the length and wingspan of the original Wright Brother’s flying machine, in feet? length: 263.25 / 12 = 21.9375 feet wingspan: 6.073 lb x lb = 1 gallon 30 gallons It weighs 182.19 lbs. 5. If you travel 336 miles on your 30 gallons of gas, what is your gas mileage? 336 miles 30 gallons = 11.2 miles per gallon 7. Fill in the table with the missing equivalents. FRACTION DECIMAL PERCENT 1 12.25 = W = 477.75 inches 39 W 477.75 / 12 = 39.8125 feet The picture should be 14.7 inches high. 3.Gasoline weighs 6.073 pounds per gallon. If you fill your gas tank with 30 gallons, how much does the gas weigh? 1 6.75 = L = 263.25 inches 39 L 4. The average height of a man in the U.S. in 2010 was 5’10”. The average weight was 191 lbs. Find the average BMI for men in the U.S. based on the average height and weight. BMI = 703W lb 703(191) 702 2 (H in) = 27.4 6. A house that costs $488,750 is 1,850 square feet. What is the price per square foot? $488,750 1,850 sq ft = $270.78 per square foot 8. Fill in the table with the missing equivalents. FRACTION DECIMAL PERCENT 1/8 0.125 12.5% 1/100 0.01 1% 1/4 0.25 25% 1/50 0.02 2% 3/8 0.375 37.5% 1/16 0.0625 6.25% 1/2 0.5 50% 39/400 0.0975 9.75% 7/8 0.875 87.5% 14/125 0.112 11.2% © 2010 Cheryl Wilcox Free Pre-Algebra Lesson 42 ! page 10 9. Leisha’s home is 1,625 square feet and she is using 450 square feet for her daycare business. To figure out her tax deduction she has to find the percent of her home’s square footage used by her business. 450 ft 2 1625 ft 2 = 0.2769... ! 28% 28% of her home is used by her business. 11. A ballot measure passed with 63% of the vote. If 276,801 people voted, how many voted in favor? 10. Shasha found that there were 1,483 songs on his iPod that he had only listened to once. His iPod held 9,447 songs. What percent of the songs had he listened to only once? 1483 songs = 0.15698... ! 16% 9447 songs About 16% of his songs. 12. Drew Brees completed 68.1% of the 658 passes he attempted in 2010. How many passes did he complete? 0.63 • 276,801 = 174,384.63 0.681 • 658 = 448.098 About 174,385 people voted in favor. He completed 448 passes. 13. You are buying a new car for $28,799. You can buy it in Sacramento, where the sales tax rate is 8.75% or in Walnut Creek, where the sales tax rate is 9.25%. How much will you save on sales tax if you buy the car in Sacramento? 14. Brittney was visiting her cousins in another state and thought the sales tax seemed low. She had bought a souvenir for $19.99 and the sales tax was $0.80. What was the sales tax rate? Sacramento: 0.0875 • $28,799 = $2,519.91 percent • 19.99 = 0.8 Walnut Creek: 0.925 • $28,799 = $2,663.91 0.8 / 19.99 = 0.04002001 You save $144 by buying in Sacramento. The sales tax rate is 4%. 15. The waiter was so funny and sweet that we decided to leave him a 20% tip. The meal cost $72.80. What was the tip? 0.2 • $72.80 = $14.56 The tip is about $14.50. 17. A new copy of the textbook costs $162.67. If a used copy is 60% off the price of a new copy, what is the used textbook price? 16. The savings of $5230 will earn 1.8% interest this year. How much will the interest be? 0.018 • $5230 = $94.14 The interest is $94.14. 18. For a limited time, you can save 30% on a gym membership. The usual price is $35 per month. What is the discounted price? 100% – 60% = 40% 100% – 30% = 70% 0.4 • $162.67 = $65.068 0.7 • $35 = $24.50 rounded to the nearest cent, $65.07. The discounted price is $24.50 The used book costs $65.07. © 2010 Cheryl Wilcox Free Pre-Algebra Lesson 42 ! page 11 Lesson 42: A Few Consumer Percents Homework 42B Name_________________________________________ 1. An iPad is 9.56 inches high by 7.47 inches wide. The giant cardboard display iPad is 5 feet wide. How high is it? 2. 1/650 Eiffel Tower Heller Plastic Model Scale: 1/650; Width: 7-1/2"; Height: 19" Find the width and height of the real Eiffel Tower in feet. 3.Gasoline weighs 6.073 pounds per gallon. If you fill your gas tank with 20 gallons, how much does the gas weigh? 4. The average height of a woman in the U.S. in 2010 was 5’4”. The average weight was 164 lbs. Find the average BMI for women in the U.S. based on the average height and weight. BMI = 703W lb (H in)2 5. If you travel 316 miles on your 20 gallons of gas, what is your gas mileage? 6. A house that costs $366,250 is 1,550 square feet. What is the price per square foot? 7. Fill in the table with the missing equivalents. 8. Fill in the table with the missing equivalents. FRACTION DECIMAL PERCENT FRACTION DECIMAL PERCENT 1/10 15% 1/5 21% 7/10 102% 91/100 8% 1/50 0.5% © 2010 Cheryl Wilcox Free Pre-Algebra Lesson 42 ! page 12 9. Sandra’s home is 1,975 square feet and she is using 780 square feet for her daycare business. To figure out her tax deduction she has to find the percent of her home’s square footage used by her business. 10. Julianne has 6,455 songs on her iPod, and 2,321 songs have been played over 20 times each. What percent of the songs have been played more than 20 times? 11. A ballot measure failed because only 37% of voters were in favor. If 276,801 people voted, how many voted in favor? 12. Drew Brees completed 70.6% of the 514 passes he attempted in 2009. How many passes did he complete? 13. You are buying a new car for $35,899. You can buy it in Sacramento, where the sales tax rate is 8.75% or in Walnut Creek, where the sales tax rate is 9.25%. How much will you save on sales tax if you buy the car in Sacramento? 14. Alisha was excited to visit Paris, but shocked to discover that the VAT (value added tax, like U.S. sales tax) was 19.6%. If she spent 85 Euros at a shop, what was the VAT on her purchase? How much did it cost in all? 15. The service was not very good, so we left a smaller tip, only $15.00 even though our meal cost $118.80. What percent did we tip? 16. The savings of $2,885 will earn 1.68% interest this year. How much will the interest be? 17. A new copy of the textbook costs $109.76. If a used copy is 45% of the new price, what is the used textbook price? 18. For a limited time, you can save 40% on a gym membership. The usual price is $42 per month. What is the discounted price? © 2010 Cheryl Wilcox

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