Multi-Part Lesson 1-3 Apply Percents PART A Main Idea Apply percents to find discount, markup, and sales tax. NGSSS MA.8.A.6.4 Perform operations on real numbers (including integer exponents, radicals percents, scientific notation, absolute value, rational numbers, and irrational numbers) using multi-step and real world problems. New Vocabulary discount markup selling price sales tax B C D Discount, Markup, and Sales Tax SALES A souvenir shop is selling beach towels for 30% off the original price. SALE! All beach towels 30% off! 1. Calculate the discount by finding 30% of $25. Regular price $25 2. What is the new cost of a beach towel? 3. Multiply 0.70 and 25. How does the result compare to your answer in Exercise 2? Discount is the amount by which a regular price is reduced. You can find the sale price of an item by subtracting the discount from the original price. Find the Sale Price glencoe.com MUSIC The CD Discount Superstore is advertising a 20% off sale. Jonas wants to buy a CD that originally costs $18.50. Find the sale price of the CD. Method 1 Find the amount of the discount first. The percent is 20%, and the whole is 18.50. We need to find the amount of the discount, or the part. Let d represent the amount of discount. d = 0.20 · 18.50 Write the percent equation. d = 3.70 Multiply. Subtract the amount of the discount from the original price to find the sale price. $18.50 - $3.70 = $14.80. Method 2 Find the percent paid first. If the amount of the discount is 20%, the percent paid is 100% - 20% or 80%. Find 80% of $18.50. Let s represent the sale price. s = 0.80 · 18.50 Write the percent equation. s = 14.80 Multiply. The sale price of the CD is $14.80. 64 Chapter 1 Rational Numbers and Percent Find the sale price of each item to the nearest cent. a. CD: $14.50, 10% off b. sweater: $39.95, 25% off A store sells an item for more than it paid for that item. The extra money is used to cover the expenses and to make a profit. The increase in the price is called the markup. The amount the customer pays is called the selling price. Find the Selling Price BUSINESS A bead store buys beads at wholesale prices and then prices them to sell at a 75% markup. If a strand of beads costs the store $9.14, what is the selling price for the strand? Method 1 Check for Reasonableness To estimate the selling price, think 75% of 9.14 is about 43 of 10 or 7.50. The selling price should be about $9 + $7.50, or $16.50. _ Find the amount of the markup first. The whole is $9.14. The percent is 75%. You need to find the amount of the markup, or the part. Let m represent the amount of the markup. m = 0.75 · 9.14 Multiply the percent equation. m ≈ 6.86 Multiply. Add the markup $6.86 to the store’s cost $9.14 to find the selling price. $9.14 + $6.86 = $16.00 Method 2 Find the total percent first. The customer will pay 100% of the store’s cost plus an extra 75% of the cost. Find 100% + 75% or 175% of the store’s cost. Let p represent the price. p = 1.75 · 9.14 Multiply the percent equation. p ≈ 16.00 Multiply. The selling price of the beads is $16.00. Find the selling price for each item given the percent of markup. c. digital camera: $120, d. sunglasses: $7, 55% markup 30% markup e. SHIPPING Cheng-Yu ordered a book that cost $24 from an online store. Her total with the shipping charge was $27. What was the percent of markup charged for shipping? Lesson 1-3 Apply Percents 65 Sales tax is an additional amount of money charged on certain goods and services. You can find the total cost of an item by adding the selling price and the sales tax. Find the Total Cost GAMES A board game that costs $25 is on sale for 15% off. The sales tax is 6.25%. What is the total cost of the board game? Step 1 Find the price of the game after the discount. Let d represent the total discount. part = percent · whole ⎫ ⎬ ⎭ ⎫ ⎬ ⎭ ⎫ ⎬ ⎭ Real-World Link Checkers is one of the oldest and most popular board games. A version of checkers has been played as far back as 3000 B.C. d = 0.15 · d = 3.75 25 Write the percent equation. Multiply. Subtract the discount from the original price to find the sale price. $25 – $3.75 = $21.25. Step 2 Find the amount of the sales tax. Let t represent the sales tax. part = percent · whole ⎫ ⎬ ⎭ ⎫ ⎬ ⎭ ⎫ ⎬ ⎭ t = 0.0625 · 21.25 t ≈ 1.33 Write the percent equation. Multiply. Add the sales tax to the sale price to find the total price. $21.25 + $1.33 = $22.58. f. BIKES A mountain bike is originally priced at $125. A flyer advertises the bike for 10% off. If there is a 7.85% sales tax, what is the total cost of the mountain bike? Example 1 (p. 64) Example 2 (p. 65) Example 3 (p. 66) 66 1. BICYCLES Find the sale price of a bicycle that is regularly $140 and is on sale for 40% off the original price. Find the selling price for each item given the percent of markup. 2. roller blades: $60, 35% markup 3. coat: $87, 33% markup 4. sunglasses: $25, 40% markup 5. snack mix: $7, 51% markup Find the total cost of each item to the nearest cent. 6. DVD player: $75, 25% off, 5% tax 7 shirt: $19, 10% off, 7.5% tax 8. car: $8,500, 5% off, 8.25% tax 9. trampoline: $130, 15% off, 6.75% tax Chapter 1 Rational Numbers and Percent = Step-by-Step Solutions begin on page R3. Extra Practice is on page EP4. Examples 1 and 3 (pp. 64 and 66) Find the sale price or total cost of each item to the nearest cent. 10. video game: $75, 25% discount 11. mountain bike: $399, 15% discount 12. skateboard: $119.95, 30% discount 13. earrings: $19.50, 35% discount 14. airplane ticket: $275, 6.5% tax 15. coat: $110, 7.85% tax 16. hotel room: $69.95, 5.25% tax 17. MP3 player: $220, 7.15% tax 18. SHOPPING Monica is shopping for clothes at a department store. Before tax, her bill is $95. a. She has a coupon to receive an additional 25% off her total purchase. What is the total cost of her items before tax? b. After she receives the discount, how much will her total bill be if there is a 7.95% sales tax? Example 2 (p. 65) B Find the selling price for each item given the cost to the store and the markup. 19. computer: $700, 30% markup 20. CD player: $120, 20% markup 21. jeans: $25, 45% markup 22. baseball cap: $12, 48% markup 23 ALGEBRA Students receive a 20% discount off the price of an adult ticket at the theater. If a student ticket is $6.80, find the price of an adult ticket. Find the percent of discount given the original price and sale price of each item. 24. coat: original price: $65 sale price: $42.25 25. shoes: original price: $90 sale price: $67.50 26. GRAPHIC NOVEL Refer to the graphic novel frame below for Exercises a–c. Coupons can save you so much money! a. Find the sale price of the sweater. b. What is the price of the sweater after the 25% off coupon is used? c. Jasmine thinks that because the sweater is 50% off and there is a 25% off coupon, the sweater is 75% off. Find the cost of the sweater if it is 75% off. Compare this answer to your answer from part b. Lesson 1-3 Apply Percents 67 C 27. CHALLENGE Jordyn purchased a sweater which originally cost $x. The sale price was 20% off the retail, and she had a coupon which took an additional 15% off the sale price. Sales tax of 6.5% was added to the cost at the end. Write the final cost of the sweater in terms of x. 28. REASONING Should the sales tax always, sometimes, or never be calculated first when dealing with discounts? Explain your reasoning. 29. NGSSS Practice Explain the difference between discount and markup. MA.7.A.1.2, MA.8.A.6.4 30. A television was originally priced at $1,250. It is now on sale. E *'f n1 f]] What is the sale price of the television? A. $875 C. $425 B. $675 D. $375 31. Grace and her two brothers shared the cost of a new video game system equally. The original price of the system was $179. They received a 15% discount off the original price and paid 7.5% sales tax on the discounted price. Find the approximate amount that each paid for the video game system. 32. Solve each equation using a percent equation. F. $51 H. $60 G. $55 I. SHORT RESPONSE Pancho paid $36 for a video game that was originally priced at $45. What was the percent of discount? (Lesson 1-2C) 33. Find 40% of 45. 34. What percent of 110 is 44? 35. 60 is 40% of what number? 36. What is 20% of 180? 37. SCHOOL A recent survey asked parents to grade themselves based on their involvement in their children’s education. The results are shown at the right. (Lesson 1-2B) a. Write the percent of parents who gave themselves an A as a decimal and as a fraction in simplest form. 2 b. Did more or less than _ of parents give themselves a B? 5 68 Chapter 1 Rational Numbers and Percent $66 Parent Survey 35% A(Superior) 44% B(Above Average) 19% C(Average) D(Below Average) 1% F(Failing) 1% Multi-Part Lesson 1-3 Apply Percents PART Main Idea Solve problems involving simple and compound interest. NGSSS MA.8.A.6.4 Perform operations on real numbers (including integer exponents, radicals, percents, scientific notation, absolute value, rational numbers, and irrational numbers) using multi-step and real world problems. New Vocabulary interest simple interest principal compound interest glencoe.com A B C D Financial Literacy: Interest CARS Have you ever dreamed of buying your first car? Suppose you want to buy a used car that costs $4,000. You can pay $400 now and borrow the remaining $3,600. To pay off the loan, you will pay $131.50 each month for the next 36 months. 1. How much money will you pay in all for the car? 2. How much will it cost you to borrow the money for the car? Interest is the amount of money paid or earned for the use of money. For a savings account, you earn interest from the bank. For a credit card or a loan, you pay interest to the bank. Simple interest is paid only on the initial principal of a savings account or loan. To solve problems involving simple interest, use the following formula. Interest is the amount of money paid or earned. The annual interest rate is expressed as a decimal. = The principal is the amount of money invested or borrowed. The time is written in years. Find Simple Interest Find the simple interest for $500 invested in a savings account at 3.25% for 3 years. I = prt Write the simple interest formula. I = 500 · 0.0325 · 3 Replace p with 500, r with 0.0325, and t with 3. I = 48.75 The simple interest is $48.75. Find the simple interest to the nearest cent. a. $400 at 3.67% for 2 years b. $770 at 16% for 6 months Lesson 1-3 Apply Percents 69 Find the Interest Rate STUDENT LOANS Luis makes monthly payments of $290.28 on his _ loan of $5,000. He plans to pay it off in 1 1 years. Find the simple 2 interest rate of his loan. First find the total that Luis will pay. 1 years = 18 months $290.28 · 18 = $5,225.04 1_ 2 He will pay $5,225.04 - $5,000 or $225.04 in interest. So, I = 225.04. Real-World Link The average cost of one year at a public university is over $11,000. Financial aid such as scholarships, grants, loans, and work study can help students pay for this. I = prt Write the simple interest formula. 225.04 = 5,000 · r · 1.5 Replace I with 225.04, p with 5,000, and t with 1.5. 225.04 = 7,500r Simplify. 7,500r 225.04 _ =_ Divide each side by 7,500. 7,500 7,500 0.03 = r The simple interest rate is 0.03 or 3%. c. SAVINGS BOND Louie purchased a $200 savings bond. After 5 years, it is worth $232.50. Find the simple interest rate for his bond. Compound interest is paid on the initial principal and on interest earned in the past. Find the Total Amount How much money is in an account where $1,500 is invested at an interest rate of 5.75% compounded annually for 2 years? Find the amount of money in the account at the end of the year 1. I = prt I = 1,500 · 0.0575 · 1 I = 86.25 Write the simple interest formula. Substitution Simplify. 1,500 + 86.25 = 1,586.25 Add the amount invested and the interest. Find the amount of money in the account at the end of year 2. I = prt Write the simple interest formula. I = 1,586.25 • 0.0575 • 1 Substitution I = 91.2094 Simplify. So, after 2 years there is $1,586.25 + $91.21 or $1,677.46. d. What is the total amount in an account where $875 is invested at an interest rate of 12% compounded annually for 3 years? 70 Chapter 1 Rational Numbers and Percent Example 1 (p. 69) Example 2 (p. 70) Example 3 (p. 70) Find the simple interest to the nearest cent. 1. $300 at 7.5% for 5 years 2. $230 at 12% for 8 months 3. CAR SALES Keisha borrowed $4,000 to buy a car. If her monthly payments are $184.17 for 2 years, what is the simple interest rate for her loan? Find the total amount in each account to the nearest cent, if the interest is compounded annually. 4. $660 at 5.25% for 2 years 5. $385 at 12.6% for 4 years 6. Nina invested $1,000 in an account for 3 years. Find the total amount if the interest is compounded annually at a rate of 2.75%. = Step-by-Step Solutions begin on page R3. Extra Practice is on page EP4. Example 1 (p. 69) Find the simple interest to the nearest cent. 7. $250 at 6% for 3 years 9. $834 at 7.25% for 2 months Example 2 (p. 70) 8. $725 at 4.5% for 4 years 10. $3,070 at 8.65% for 24 months 11. BASEBALL CARDS The prices for a vintage baseball card are given at the right. Determine the simple interest rate for a card purchased as an investment in 1968 and sold in 2011. Year Price for Baseball Card 1968 $18.00 2011 $325.80 12. SAVINGS Colin is borrowing money from his parents to purchase a $700 computer. He will pay them $35 per month for two years. Determine the simple interest rate on Colin’s loan. Example 3 (p. 70) B Find the total amount in each account to the nearest cent, if the interest is compounded annually. 13 $2,250 at 5% for 3 years 14. $5,060 at 7.2% for 2 years 15. $575 at 4.25% for 18 months 16. $950 at 7.85% for 3 years 17 CARS Felicia took out a 5-year loan for $15,000 to buy a car. If the interest is compounded annually at a rate of 11%, how much will she pay in all? Find the simple interest to the nearest cent. 1 18. $1,000 at 7_ % for 30 months 2 1 1 19. $5,200 at 13_ % for 1_ years 5 2 20. CREDIT CARDS The balance on a credit card was $500. Mrs. Cook paid the minimum monthly payment of $25. The remaining balance was charged a simple interest rate of 18%. If no additional purchases were made, what was the balance the next month? 21. HOUSING The Turners need to borrow $100,000 to purchase a home. The credit union is offering a 30-year mortgage loan at 5.38% interest while the community bank has a 25-year mortgage loan at 6.12% interest. Assuming simple interest, which loan will result in less total interest? Lesson 1-3 Apply Percents 71 C 22. CHALLENGE What will be the monthly payments on a loan of $25,000 at 9% simple interest so that it will be paid off in 15 years? How much will the total interest be? 23. OPEN ENDED Give a principal and interest rate where the amount of simple interest earned in 6 months is more than $100. 24. NGSSS Practice If you have money in a savings account for 8 months, what value for t would you use in the formula I = prt to find the interest you have earned? Explain. MA.8.A.6.4 25. Mrs. Owens placed $1,500 in a college savings account with a simple interest rate of 4% when Lauren was born. How much will be in the account in 18 years when Lauren is ready to go to college? Assume no more deposits or withdrawals are made. 26. Dave borrowed $4,000 from the bank at an interest rate of 9%. The interest is compounded annually. Suppose he made no payments, approximately how much would he owe at the end of three years? F. $1,080 A. $1,080 G. $1,180 B. $2,580 H. $5,080 C. $10,800 I. $5,180 D. $12,300 27. DISCOUNT A watch that regularly sells for $35 is on sale for $26.95. Find the percent of discount. (Lesson 1-3A) 28. COLORS The table lists the number of each color of candies in a jar. (Lesson 1-2C) Color Number Brown 12 a. What percent of the candies are brown? Green 5 b. What percent of the candies are green? Yellow 4 Red 2 Orange 1 Blue 1 1 29. Order the set of numbers _ , 16%, and 0.016 from 6 least to greatest. (Lesson 1-2B) 3 30. VEGETABLES Hudson purchased 3_ pounds of vegetables 8 that cost $3 per pound. What was the total cost of the vegetables? Add. (Lesson 0-3) 31. -48 + 13 + (-16) 32. 35 + 17 + (-25) 33. -50 + (-62) + 3 34. 27 + (-30) + (-26) 72 Chapter 1 Rational Numbers and Percent (Lesson 1-1C) Multi-Part Lesson 1-3 Apply Percents PART A B C D Spreadsheet: Main Idea Compound Interest Find compound interest. You can use a spreadsheet to investigate compound interest. NGSSS MA.8.A.6.4 Perform operations on real numbers (including integer exponents, radicals, percents, scientific notation, absolute value, rational numbers, and irrational numbers) using multi-step and real world problems. glencoe.com The spreadsheet evaluates the formula A4 × B1. Find the value of a $2,000 savings account after four years if the account pays 8% interest compounded semiannually. 8% interest compounded semiannually means that the interest is paid twice a year. The interest rate is 8% ÷ 2 or 4% every 6 months. $PNQPVOE*OUFSFTU # $ % " 3BUF *OUFSFTU /FX1SJODJQBM 5JNF:3 1SJODJQBM 4IFFU 4IFFU The interest rate is entered as a decimal. The interest is added to the principal every 6 months. The spreadsheet evaluates the formula A4 + B4. 4IFFU The value of the savings account after four years is $2,737.14. and Apply 1. Use a spreadsheet to find the value of a savings account if $2,000 is invested for four years at 8% interest compounded quarterly. 2. Suppose you leave $1,000 in each of three bank accounts paying 6% interest per year. One account pays simple interest, one pays interest compounded semiannually, and one pays interest compounded quarterly. Use a spreadsheet to find the amount of money in each account after three years. 3. MAKE A CONJECTURE How does the amount of interest change if the compounding occurs more frequently? Explain your reasoning. Lesson 1-3 Apply Percents 73 Multi-Part Lesson 1-3 Apply Percents PART Main Idea Find and use the percent of increase or decrease. NGSSS MA.8.A.6.4 Perform operations on real numbers (including integer exponents, radicals, percents, scientific notation, absolute value, rational numbers, and irrational numbers) using multi-step and real world problems. A B D C Percent of Change STAMPS Over the years, the price of stamps has increased. Refer to the table that shows the change in stamp prices from 1963 to 1981. Price of a Stamp Effective Date Price for the First Ounce (¢) January 7, 1963 5 March 2, 1974 10 May 29, 1978 15 November 1, 1981 20 1. How much did the price increase from 1963 to 1974? amount of increase 2. Write the ratio __ . Then write the ratio as a percent. price in 1963 New Vocabulary percent of change percent of increase percent of decrease 3. How much did the price increase from 1974 to 1978? Write the amount of increase ratio __ . Then write the ratio as a percent. price in 1974 4. How much did the price increase from 1978 to 1981? Write the amount of increase ratio __ . Then write the ratio as a percent. price in 1978 glencoe.com 5. MAKE A CONJECTURE Why are the amounts of increase the same but the percents different? The percent that an amount changes from its original amount is called the percent of change. Percent of Change Words A percent of change is a ratio that compares the change in quantity to the original amount. Symbols percent of change = amount of change __ original amount To find the percent of change, do the following: Step 1 Subtract the original amount from the final amount to find the amount of change. amount of change original amount Step 2 Write the ratio __ as a decimal. Step 3 Write the decimal as a percent. 74 Chapter 1 Rational Numbers and Percent When the percent is positive, the percent of change is a percent of increase. When the percent is negative, the percent of change is called a percent of decrease. Percent of Change When finding percent of change, always use the original amount as the whole. Find Percent of Change YEARBOOKS Last year Wesley Middle School sold 174 yearbooks. This year they sold 200 yearbooks. Find the percent of change. Round to the nearest tenth if necessary. State whether the change is an increase or decrease. Step 1 Subtract to find the amount of change. 200 - 174 or 26. final amount - original amount amount of change Definition of percent Step 2 percent of change = __ of change original amount = 26 _ Substitution Divide. Use a calculator. 174 ≈ 0.1494252 Step 3 0.1494252 =14.94252% or 14.9%. Since the percent of change is positive, it is a percent of increase. WEATHER On average, Florida has 54 inches of rainfall per year, but in 2007, it had only 45 inches of rainfall. Find the percent of change. Round to the nearest tenth if necessary. State whether the change is an increase or decrease. Step 1 Subtract to find the amount of change. 45 - 54 or -9 final amount - original amount amount of change original amount Step 2 percent of change = __ =_ Substitution − ≈ -0.16 Divide. Use a calculator. -9 54 Real-World Link The National Oceanic and Atmospheric Administration or NOAA is the government agency responsible for monitoring the weather in the United States. The agency is able to monitor storms such as hurricanes from the sky. Definition of percent of change Step 3 Express the ratio as a percent. −− -0.16 = -16.666...% or -16.7% Since the percent of change is negative, it is a percent of decrease. Find each percent of change. Round to the nearest tenth if necessary. State whether the percent of change is an increase or a decrease. a. original: 6 hours new: 10 hours b. original: 80 water bottles new: 55 water bottles Lesson 1-3 Apply Percents 75 Examples 1 and 2 (p. 75) Find each percent of change. Round to the nearest tenth if necessary. State whether the percent of change is an increase or a decrease. 1. original: $40 new: $32 2. original: 25 CDs new: 32 CDs 3 original: 325 miles new: 400 miles 4. BOWLING Inez bowled a 127 her first game. In her second game, she bowled a 145. Find the percent of change. Round to the nearest tenth if necessary. State whether the change is an increase or a decrease. = Step-by-Step Solutions begin on page R4. Extra Practice is on page EP5. Examples 1 and 2 (p. 75) Find each percent of change. Round to the nearest tenth if necessary. State whether the percent of change is an increase or a decrease. 5. original: 6 tickets new: 9 tickets 6. original: 27 guests new: 39 guests 8. original: $560 new: $420 9. original: 68°F new: 51°F 7. original: $80 new: $64 10. original: 150 e-mails new: 98 e-mails 11. TELEVISION On Tuesday night, 17.8 million households watched a popular television show. On Wednesday night, 16.6 million households watched the same show. Find the percent of decrease in the number of households watching the show from Tuesday to Wednesday. 12. STOCK Patrice invested $300 in a particular stock. The amount doubled within a few weeks. Find the percent of increase. B 13 INTERNET An Internet service provider offers a connection speed that is 35% faster than dial-up. If it takes Brad 8 seconds to connect to the Internet using dial-up, how long would it take using this provider? 14. GRAPHIC NOVEL Refer to the graphic novel frame below for Exercises a–b. I can’t believe how much the original price changed. Another great deal! We should come here more often. a. What is the price of the shirt if Alma uses the 25% off coupon? b. Find the percent of change from the original price. Is the percent of change a percent of increase or decrease? 76 Chapter 1 Rational Numbers and Percent C 15. OPEN ENDED Give an example of a real-world situation where a percent of change occurs. 16. CHALLENGE The percent of change over Ethan’s last three test scores is 15%. If he scored a 92 on the last test, what are possible scores for the first two tests? 17. NGSSS Practice Write and solve a real-world problem involving a 25% increase or decrease in some quantity. MA.8.A.6.4 18. On Monday, the high temperature was 66°F. On Wednesday, it was 79°F. What was the percent of change? A. -19.7% C. 16.5% B. -16.5% D. 19.7% 20. Which of the following represents the greatest percent of decrease? A. A pair of jeans originally priced at $22 on sale for $15. B. The number of pages left to read decreased from 281 to 180 pages. 19. If the dimensions of the square below are doubled, what is the percent of increase in the area of the square? C. The paper route went from 45 houses to 30 houses. D. Attendance decreased from 176 on Friday to 114 on Saturday. 5.5 cm 5.5 cm F. 100% H. 300% G. 200% I. 400% 21. SAVINGS The Millers opened a savings account for their newborn son with $430. Find the total amount in the account after 3 years if the simple interest rate is 2.5%. (Lesson 1-3B) 22. SALES What is the sale price of a $200 cell phone on sale at 10% off the regular price? (Lesson 1-3A) GEOMETRY Find the perimeter of each figure. 23. 1 ft 2 1 1 2 ft (Lesson 1-1B) 24. 1 5 2 6 in. 1 6 in. 1 3 6 in. Lesson 1-3 Apply Percents 77
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