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Online Instructor’s Solutions Manual for Mathematics for Business Tenth Edition Stanley A Salzman American River College Gary Clendenen Sienna College Prepared by Deana Richmond Boston Columbus Indianapolis New York San Francisco Upper Saddle River Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montreal Toronto Delhi Mexico City Sao Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo Copyright © 2014 by Pearson Education, Inc All rights reserved Manufactured in the United States of America This publication is protected by Copyright, and permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise To obtain permission(s) to use material from this work, please submit a written request to Pearson Education, Inc., Permissions Department, Lake Street, Upper Saddle River, New Jersey 07458, or you may fax your request to 201-236-3290 Many of the designations by manufacturers and seller to distinguish their products are claimed as trademarks Where those designations appear in this book, and the publisher was aware of a trademark claim, the designations have been printed in initial caps or all caps 10 ISBN13: 978-0-13-3251616 ISBN10: 0-13-3251616 Chapter 1.1 Problem Solving and Operations with Fractions 14 $625 - $75 = $550 $550´ = $2200 The amount saved is $2200 Problem Solving 80 + 75 + 135 + 40 + 52 = 382 Beth rode 382 miles 15 (6´$1256) + (15´$895) = $20,961 325 + 75 + 137 + 495 + 105 = 1137 1137 pounds of these coffees were sold The total cost is $20,961 16 (23´$479) + (8´$247) = $12,993 1815 -1348 = 467 467 passengers remain on the ship The total cost is $12,993 17 1250 - (30´ 25) = 500 $250, 000 - $15, 000 = $235, 000 There is $235,000 more in the large machines than in the small machines There are 500 balcony seats 500 ¸ 25 = 20 There must be 20 seats in each row 2.5 - 0.8 = 1.7 The required reduction is 1.7 billion tons 18 (24´30) ¸ = 120 A total of 120 boxes of wreaths are shipped 397,012 - 364,383 = 32,629 The decrease in the rate at which world population is growing is 32,629 people per day 120 ¸ = 24 Each shop will receive 24 boxes 19 4.4´8 = 35.2 35.2 hours would be needed 2425 - 582 + 634 = 2477 The car will weigh 2477 pounds 20 $2679.99´14 = $37,519.86 The cost is $37,519.86 $2324 - $734 + $568 = $2158 The balance in the account is $2158 21 38 ¸ 0.58 » 65.5 There are 65.5 million shares 24, 000, 000 - 7000 = 23,993, 000 There are 23,993,000 small and midsize businesses 22 42 ¸ 0.65 » 64.6 » 65 There are 65 million shares (rounded) 10 21,375 - 9250 = 12,125 The weight of the firewood is 12,125 pounds 23 221 8.359 26 26 coins can be produced 11 900´365 = 328,500 328,500 World War II veterans are projected to die in the next year 24 57.13 1.62 35 35 dosages can be made 12 $30, 000´12, 600 = 378, 000, 000 The total cost would be $378,000,000 25 (a) 100 0.0043 0.43 The pile is 0.43 inch high (b) 1000 0.0043 4.3 The pile is 4.3 inches high 13 $239 - $89 = $150 $150´5 = $750 The amount saved is $750 Chapter Problem Solving and Operations with Fractions 26 (a) 43 0.0043 10, 000 There are 10,000 bills (b) 10, 000 $20 $200, 000 You would have $200,000 17 141 17 8 8 8 16 16 10 15 15 20 20 11 40 40 75 75 15 12 36 36 6 42 42 13 25 25 5 40 40 29 $246,500 0.06 $14, 790 The commission was $14,790 14 27 27 45 45 30 6.5 $8.70 $56.55 Her total cost was $56.55 15 120 120 30 150 150 30 16 24 24 64 64 8 17 132 132 12 11 144 144 12 12 14 5 18 40 40 96 96 12 4 17 4 19 96 96 12 180 180 12 15 11 30 11 11 11 20 32 32 32 128 128 32 27 (a) 42 4.3 180.6 The manager worked 180.6 hours each month (b) $3250 180.6 $18.00 The manager earned $18.00 per hour 28 (a) 48 4.3 206.4 The assistant manager worked 206.4 hours each month (b) $3539.76 206.4 $17.15 The assistant manager earned $17.15 per hour 1.2 Addition and Subtraction of Fractions 1 2 4 1 8 11 22 183 22 8 15 3 47 15 3 12 101 12 8 21 1 22 =3 2 =1 5 Chapter Problem Solving and Operations with Fractions 23 20 76 60 16 24 15 42 30 12 25 11 14 11 26 55 48 27 15 21 15 28 52 85 52 33 29 64 124 64 60 30 35 190 175 15 31 32 81 64 17 32 64 360 320 40 76 16 =3 =3 20 20 33 Answers will vary 34 Answers will vary 35 2 +1 + = = 5 5 36 2+4 + = = = 9 9 37 14 14 + 17 + = + = = 10 20 20 20 20 20 38 3 3+ + = + = = 8 8 39 35 32 35 + 32 67 + = + = = =1 12 15 60 60 60 60 60 40 15 14 15 + 14 29 + = + = = =1 12 24 24 24 24 24 41 18 18 + 19 + = + = = 11 22 22 22 22 22 42 15 14 15 + 14 29 11 + = + = = =1 18 18 18 18 18 42 12 =2 =2 15 15 14 =1 11 11 55 =6 8 21 =1 =1 15 15 85 33 =1 52 52 43 124 60 15 =1 =1 64 64 16 190 15 =5 =5 35 35 44 81 17 =2 32 32 45 360 40 =5 =5 64 64 46 27 20 12 + + = + + 36 36 36 27 + 20 + 12 59 23 = = =1 36 36 36 1 + + = + + 12 24 24 24 + + 11 = = 24 24 5 20 18 15 + + = + + 24 24 24 20 + 18 + 15 53 = = =2 24 24 24 21 16 25 + + = + + 10 15 30 30 30 21 + 16 + 25 62 = = =2 =2 30 30 30 15 47 48 49 50 51 52 Chapter Problem Solving and Operations with Fractions + 15 97 82 53 + 14 39 54 25 1 51 = 51 4 + 29 = 29 80 15 = 38 18 29 = 29 18 + 47 = 47 18 30 12 12 114 = 114 + = 115 = 115 18 18 18 38 18 = 32 24 = 24 15 + 14 = 14 24 41 17 17 52 = 52 + = 53 24 24 24 32 28 = 16 10 40 26 = 26 40 15 +8 = 8 40 51 11 11 50 = 50 + = 51 40 40 40 16 5 = 89 9 10 = 10 1 + 87 = 87 9 186 = 186 + = 187 89 14 = 74 70 30 58 = 58 70 21 + 21 = 21 10 70 65 13 153 = 153 70 14 74 55 - = = 8 56 11 - = = 12 12 12 57 4 -1 - = - = = = 6 6 58 7 7-4 - = - = = 8 8 59 20 17 - = - = 12 16 48 48 48 60 15 14 15 -14 - = - = = 18 18 18 18 61 9-5 - = - = = = 12 12 12 12 12 62 15 15 - - = - = = 21 21 21 21 63 = 16 3 - 12 = 12 8 16 Chapter Problem Solving and Operations with Fractions 64 65 66 67 68 13 13 = 25 24 24 10 - 18 = 18 12 24 =7 24 25 21 =9 24 10 -6 =6 12 24 11 24 15 = 24 18 10 - 18 = 18 18 18 24 71 = 71 24 - 62 = 62 24 24 10 = 19 12 - 12 = 12 12 12 19 69 19 = 18 3 - 12 = 12 4 70 6 5 - 211 = 211 6 162 374 = 373 71 Answers will vary 72 Answers will vary 73 Answers will vary 74 Answers will vary 75 1 10 16 + + = + + 40 40 40 + 10 + 16 31 = = 40 40 The total length of the screw is 76 31 inch 40 1 12 20 15 + + = + + 60 60 60 12 + 20 + 15 47 = = 60 60 The total length of the bolt is 47 inch 60 21 12 16 77 + + + = + + + 3 24 24 24 24 57 =2 =4 =4 24 24 The total distance around the wetlands reserve is miles 7 16 78 + + + = 28 = 30 8 8 The length of trim needed is 30 inches 79 80 15 ổỗ 3 ửữ 15 15 12 - ỗ + ữữ = - = - = ỗ 16 è 8 ø 16 16 16 16 The diameter of the hole is inch 16 ổỗ 1 ửữ ổỗ ửữ -ỗ + ữ = -ỗ + ữ = çè ø÷ èç 6 ø÷ 7 = - = - = 8 8 liter of fluid remaining There is 8 Chapter Problem Solving and Operations with Fractions 1 81 + + + 4 = +6 +3 +7 4 = 21 = 22 = 22 Hernando drove 22 hours 82 + + + 16 = + + +1 16 16 16 16 23 = 13 = 14 16 16 A total of 14 tons of vegetables were sold 16 æ 3ử 83 -ỗỗ2 + + ữữữ ỗ è 4ø ỉ 3ư = - ỗỗ2 + + ữữữ ỗ ố 4ứ ổ 5ử = -ỗỗ6 ữữữ çè ø ỉ 1ư = -çç7 ÷÷÷ ỗố ứ ổ 2ử = -ỗỗ7 ữữữ = ỗố ứ cubic yards of concrete remain in the truck ổ 7ử 84 15 - ỗỗ3 + + ữữữ ỗố 8ứ ổ 7ử = 15 - ỗỗ3 + + ữữữ çè 8 8ø ỉ 14 = 15 - çç10 ÷÷÷ çè ø ỉ 6ư = 15 -çç11 ữữữ ỗố ứ = 14 -11 = 4 There are yards of material remaining 1 85 + + + 4 = +5 +3 +6 12 12 12 12 22 = 18 12 10 = 18 + 12 = 18 + = 19 A total of 19 cases were sold 3 86 + + + + 4 = +5 +4 +3 +6 8 8 = 21 15 = 21 + = 22 8 Altogether, Andrea worked 22 hours ỉ 1 3ư 87 40 - ỗỗ8 + + + ữữữ ỗố 4ứ ổ 9ử = 40 - ỗỗ8 + + + ữữữ ỗố 12 12 12 12 ứ ổ 22 = 40 - ỗỗ29 ữữữ ỗố 12 ứ ổ 10 = 40 -ỗỗ30 ữữữ ỗố 12 ứ ổ 5ử = 40 -ỗỗ30 ữữữ ỗố ứ = 39 - 30 6 =9 Julie worked hours on Friday Chapter Problem Solving and Operations with Fractions 3 88 34 + 23 + 34 + 23 4 3 = 34 + 23 + 34 + 23 4 4 10 = 114 = 116 = 116 The length needed is 116 inches 1.3 5´1 = ´ = ´ 12 1´1 ´ = = 8´ 16 3 ổ 1ử 89 518 - ỗỗ108 + 162 + 143 ữữữ ỗố 2ứ 2 14 2´14 = 28 6´ = ´ ´= 1´1 3 feet ổỗ 16 18 15 - ỗ107 + 150 + 138 ữữữ ỗ 24 ố 24 24 24 ứ ổỗ 49 - ỗ395 ữữữ ỗ 24 è 24 ø 1 527 - 397 24 24 = 130 The length of the fourth side is 130 feet = 527 1 ổỗ 5ử - ỗ107 + 150 + 138 ữữữ 24 ỗố 8ø = 527 27 1´9 = = =4 ´ = ´ 10 10 1´ 2 ổ 9ử = 518 - ỗỗ413 ữữữ ỗ ố 8ứ ổ 1ử = 518 -ỗỗ414 ữữữ ỗ è 8ø = 518 - 414 8 = 104 90 527 11 9´11 99 ´ = = 10 16 10´16 160 1 5´ 35 = =4 ´3 = ´ = 4 4´ 8 ỉ 4ư = 518 - çç108 + 162 + 143 ÷÷÷ ç è 8 8ø The length of the fourth side is 104 Multiplication and Division of Fractions 23 15 23´3 = = 69 ´15 = ´ 1´1 1 8 ´ ´ = ´ ´ 9 1´ 2´5 10 = = =1 =1 1´3´ 6 5 11 ´ ´3 = ´ ´ 9 5´1´11 55 = = =4 1´ 4´3 12 12 9 13 10 ´ ´3 = ´ ´ 8 = 1´3´13 39 = =2 1´ 4´ 16 16 Chapter Problem Solving and Operations with Fractions 10 15 25 15 21 ¸ = ¸ 16 16 12 11 12´ ´3 = ´ ´ 2 = 25 16 5´ 10 = ´ = = =3 1´3 3 15 ´ 5´ = 90 1´1´1 11 22 ¸ = ¸ 2 11 11´1 11 = ´ = = =1 2´ 8 18 ´ ´ 12 18´1 ´ = 3 1 ´ 5´ = = 60 1´1´1 23 ¸ = ¸ 4 6´ 24 = ´ = = =4 5 5 1 1 1´1 = 13 ¸ = ´ = 6 2´1 2 14 5 16 5´ 10 ¸ = ´ = = =3 16 1´3 3 1 25 Answers will vary 13 26 13 30 1´3 ¸ = ´ = = 15 20 30 ´2 20 26 24 ¸ = ¸ 4 3´ 12 = ´ = = =2 5 5 26 Answers will vary 16 7 ´1 ¸ = ´ = = =1 8 2´3 6 $ $4´3 = $12 ´ = 27 $8´1 = 1´1 2 17 15 15 3´1 ¸ = ´ = = =1 16 16 2´1 2 2 12 12 22 4´ ¸ = ´ = = =8 11 22 11 1´1 1 15 1´ 2 19 ¸ = ¸ = ´ = = 4 15 1´3 3 1 13 20 ¸ = ¸ 2 2 13 13´1 13 = ´ = = = 13 1´1 1 1 18 $ 14 $7 ´3 = $21 28 $14´1 = ´ = 1´1 $17 ´ 29 $17 ´1 = 2 $17 ´3 $51 = = = $25.50 1´ 2 $9 30 $9´1 = ´ 2 $9´3 $27 = = = $13.50 1´ 2 $21 ´ 31 $10.50´1 = 2 $21´3 $63 = = = $15.75 2´ 36 Chapter Equations and Formulas 46 I = PRT ; P = $8000, T = 4, I = $1920 $1920 = $8000´ R ´ $1920 = $32, 000 R $1920 $32, 000 R = $32, 000 $32, 000 0.06 = R The interest rate was 0.06 or 6% 47 I = PRT ; P = $22, 000, T = 2, I = $5720 $5720 = $22, 000´ R ´ $5720 = $44, 000 R $5720 $44, 000 R = $44, 000 $44, 000 0.13 = R The rate of interest was 0.13, or 13% 48 I = PRT ; P = $39, 000, R = 0.07, I = $13, 650 $13, 650 = $39, 000´ 0.07 ´T $13, 650 = $2730T $13, 650 $2730T = $2730 $2730 5=T The time for the loan is years 49 I = PRT ; P = $5850, R = 0.03, I = $702 $702 = $5850´ 0.03´T $702 = $175.50T $702 $175.50T = $175.50 $175.50 4=T The time for the loan is years 50 M = P (1 + RT ); P = $1000, R = 0.04, T = M = $1000 (1 + 0.04 ⋅ 5) M = $1000 (1 + 0.2) M = $1000 (1.2) M = $1200 Mary had $1200 in her account 51 M = P (1 + RT ); M = $4560, R = 0.07, T = $4560 = P (1 + 0.07 ⋅ 2) $4560 = P (1 + 0.14) $4560 = P (1.14) $4560 1.14 P = 1.14 1.14 $4000 = P John initially deposited $4000 52 M = P (1 + RT ); M = $14, 750, P = $12,500, T = $14, 750 = $12,500 (1 + R ⋅ 2) $14, 750 = $12,500 (1 + R ) $14, 750 = $12,500 + 25, 000 R $2250 = 25, 000 R $2250 25, 000 R = 25, 000 25, 000 0.09 = R The interest rate was 9% n 53 M = P (1 + i ) ; M = $5668.20, i = 0.08, n = 3 $5668.20 = P (1 + 0.08) $5668.20 = P (1.08) $5668.20 = P (1.259712) $5668.20 1.259712 P = 1.259712 1.259712 $4499.60 = P $4500 » P The amount borrowed was $4500 n 54 M = P (1 + i ) ; P = $8500, i = 0.035, n = 20 20 M = $8500 (1 + 0.035) 20 M = $8500 (1.035) M » $8500 (1.98978886) M » $16,913.21 The maturity value is $16,913.21 55 Answers will vary 56 Answers will vary Chapter Equations and Formulas 2.4 Ratios and Proportions 18 kilometers to 64 kilometers 18 = 64 32 18 defects out of 580 items 18 = 580 290 216 students to faculty 216 27 = $80 in returns to $8360 in sales 80 = 8360 209 men to women = 12 35 dimes to dollars dollars = 60 dimes 35 = 60 12 13 20 hours to days days = 120 hours 20 = 120 14 days to hours days = 144 hours 144 16 = 15 $0.80 to $3 0.8 = = 30 15 16 $1.20 to $0.75 1.20 120 = = 0.75 75 12 feet to inch 12 feet = 144 inches 144 17 $3.24 to $0.72 3.24 324 = = 0.72 72 30 kilometers (30,000 meters) to meters 30, 000 3750 = 18 $3.57 to $0.42 3.57 357 17 = = 0.42 42 30 inches to yards yards = 180 inches 30 = 180 90 dollars to 40 cents 90 dollars = 9000 cents 9000 225 = 40 19 The proportion is true 20 10 148 minutes to hours hours = 240 minutes 148 37 = 240 60 30 = 13 65 ⋅ 65 = 13 ⋅ 30 390 = 390 The proportion is true 21 11 dollars to 10 quarters dollars = 16 quarters 16 = 10 21 = 35 ⋅ 35 = ⋅ 21 105 = 105 720 = 480 ⋅ 480 = ⋅ 720 4320 ¹ 5040 The proportion is false 37 38 22 Chapter Equations and Formulas 54 270 = 14 70 54 ⋅ 70 = 14 ⋅ 270 3780 = 3780 30 The proportion is true 23 69 = 320 102 69 ⋅102 = 320 ⋅ 7038 ¹ 2240 The proportion is true 31 The proportion is false 24 17 72 = 19 84 17 ⋅ 84 = 19 ⋅ 72 1428 ¹ 1368 28 224 = 75 600 28 ⋅ 600 = 75 ⋅ 224 16,800 = 16,800 7.6 76 = 10 100 7.6 ⋅100 = 10 ⋅ 76 760 = 760 The proportion is true 32 The proportion is false 95 320 = 64 217 95 ⋅ 217 = 64 ⋅ 320 20, 615 ¹ 20, 480 The proportion is false 19 33 = 25 32 77 19 ⋅ 77 = 32 ⋅ 33 1463 ¹ 1056 The proportion is false 26 19 57 = 30 90 19 ⋅ 90 = 30 ⋅ 57 1710 = 1710 The proportion is true 27 110 160 = 18 27 110 ⋅ 27 = 18 ⋅160 2970 ¹ 2880 The proportion is false 28 46 212 = 17 95 46 ⋅ 95 = 17 ⋅ 212 4370 ¹ 3604 The proportion is false 29 32 61 = 75 108 32 ⋅108 = 75 ⋅ 61 3456 ¹ 4575 The proportion is false 4= 20 33 ⋅ 20 = ⋅ 45 = 45 The proportion is true 34 = 80 120 ⋅120 = 80 ⋅ 90 = 90 The proportion is true = 27 35 41 1 ⋅ 41 = ⋅ 27 4.2 ⋅ 41 = 6.125 ⋅ 27 172.2 ¹ 165.375 The proportion is false Chapter Equations and Formulas 1 2= 12 42 36 42 1 ⋅ 42 = 12 ⋅ 1.5 ⋅ 42 = 12 ⋅ 5.25 63 = 63 16t 4592 = 16 16 t = 287 The proportion is true 37 8.15 61.125 = 2.03 15.225 8.15 ⋅15.225 = 2.03 ⋅ 61.125 124.08375 = 124.08375 43 423.88 330.6264 = 17.119 13.35282 423.88 ⋅13.35282 = 17.119 ⋅ 330.6264 5659.993342 = 5659.993342 315 3s = 3 105 = s 44 780 390 x = 390 390 2= x x 49 = 15 105 x ⋅105 = 15 ⋅ 49 105 x = 735 45 105 x 735 = 105 105 x=7 40 2r = 2 =r 315 y = 945 41 r = 108 ⋅108 = ⋅ r 648 = 9r 648 9r = 9 72 = r r = 1⋅ = ⋅ r = 2r y 27 = 35 315 y ⋅ 315 = 35 ⋅ 27 315 y 945 = 315 315 y=3 260 x = 390 260 ⋅ = 390 ⋅ x 780 = 390 x The proportion is true 39 63 = s 63 ⋅ = s ⋅ 315 = 3s The proportion is true 38 16 112 = 41 t 16 ⋅ t = 41⋅112 16t = 4592 46 = s ⋅ s = 3⋅ 2s = 15 2s 15 = 2 s=7 39 40 47 Chapter Equations and Formulas 4=3 x ⋅ x = 6⋅3 x = 18 4 ⋅ x = ⋅18 x = 24 48 11 = x ⋅ = x ⋅11 27 = 11x 27 11x = 11 11 27 =x 11 =x 11 49 12 23.571 = p 15.714 12 ⋅15.714 = p ⋅ 23.571 188.568 = 23.571 p 188.568 23.571 p = 23.571 23.571 8= p 50 86.112 k = 57.408 15 86.112 ⋅15 = 57.408 ⋅ k 1291.68 = 57.408k 1291.68 57.408k = 57.408 57.408 22.5 = k 51 Answers will vary 52 Answers will vary 53 x = number of tickets it can expect to sell in days Set up and solve a proportion 350 = x ⋅ x = ⋅ 350 x = 3150 x = 1575 It can expect to sell 1575 tickets in days 54 x = number of blood cells in a 140-pound person Set up and solve a proportion 170 30 = x 140 170 ⋅ x = 140 ⋅ 30 170 x = 4200 x » 24.7 There are approximately 24.7 trillion blood cells in a 140-pound person 55 x = cost for a 12-unit apartment house Set up and solve a proportion 215, 000 = 12 x ⋅ x = 12 ⋅ 215, 000 x = 2,580, 000 x = 516, 000 The cost for a 12-unit apartment house is $516,000 56 x = number of pounds of meat that a 360pound tiger eats per day Set up and solve a proportion 450 15 = 360 x 450 ⋅ x = 360 ⋅15 450 x = 5400 x = 12 You would expect a 360-pound tiger to eat 12 pounds of meat per day 57 x = cost of 12 dresses Set up and solve a proportion 22 660 = 12 x 22 ⋅ x = 12 ⋅ 660 22 x = 7920 x = 360 The cost of 12 dresses is $360 58 x = amount of flour needed to make biscuits for 125 people Set up and solve a proportion 125 = x ⋅ x = ⋅125 x = 250 x » 36 Approximately 36 cups of flour are needed for biscuits to feed a church group of 125 Chapter Equations and Formulas 41 59 x = number of red sports models produced Set up and solve a proportion x = 868 ⋅ 868 = ⋅ x 2604 = x 372 = x There are 372 red sports models produced 64 x = amount that goes to Chester Set up and solve a proportion x = 45, 000 ⋅ 45, 000 = ⋅ x 90, 000 = x 60 x = number of sacks needed to cover 7125 square feet Set up and solve a proportion 3325 = 7125 x 3325 ⋅ x = 7125 ⋅ 3325 x = 49,875 x = 15 15 sacks are needed for 7125 square feet 65 x = profits for the second partner Set up and solve a proportion 48, 000 = x ⋅ x = ⋅ 48, 000 3x = 384, 000 x = 128, 000 The profit earned by the second partner is $128,000 61 x = distance between the two other cities Set up and solve a proportion 120 = 17 x ⋅ x = 17 ⋅120 x = 2040 x = 1020 The cities are 1020 miles apart 66 x = number of production employees Set up and solve a proportion 24 = x ⋅ x = ⋅ 24 x = 168 x = 84 There are 84 production employees 62 x = sales for the first weeks Set up and solve a proportion 3720 = x ⋅ x = ⋅ 3720 3x = 14,880 x = 4960 Sales for the first weeks were $4960 67 x = distance eider ducks migrate in the amount of time it takes songbirds to migrate 200 miles Set up and solve a proportion 20 200 = 35 x 20 ⋅ x = 35 ⋅ 200 20 x = 7000 x = 350 Eider ducks migrate 350 miles in the same amount of time it would take songbirds to migrate 200 miles 63 x = sales for the entire 52-week year Set up and solve a proportion 20 $274,312 = 52 x 20 ⋅ x = 52 ⋅ $274,312 20 x = $14, 264, 224 x = $713, 211.20 Sales for the entire year are $713,211.20 18, 000 = x $18,000 goes to Chester 68 x = number of islands Set up and solve a proportion 741,101 13, 677 = 3, 618, 770 x 741,101⋅ x = 3, 618, 770 ⋅13, 677 741,101x = 49, 493,917, 290 x » 66, 784 There would be about 66,784 islands 42 Chapter Equations and Formulas 69 x = amount of an iceberg that is underwater Set up and solve a proportion = 500, 000 x ⋅ x = ⋅ 500, 000 8 x = 437,500 8 ⋅ x = ⋅ 437,500 x = 3,500, 000 3,500,000 cubic meters of the iceberg is underwater 2.5 Exponents and the Order of Operations p ⋅ p = p 2 ⋅ = 32 r ⋅ r ⋅ r = r ⋅ ⋅ = 73 x ⋅ x ⋅ x ⋅ x = x 5´5´5 = 53 72 = ⋅ = 49 70 x = increase in global average temperature Set up and solve a proportion 380 - 315 550 - 380 = x 65 170 = x 65 ⋅ x = 1⋅170 65 x = 170 x » 2.6 There is a further increase of 2.6 Fahrenheit 71 x = number of U.S dollars he will receive Set up and solve a proportion 80 = 20, 355 x 80 ⋅ x = 20, 355 ⋅1 80 x = 20, 355 x » 254.44 Benjamin will receive U.S $254.44 72 x = salary in U.S dollars Set up and solve a proportion 7.25 = 471, 200 x 7.25 ⋅ x = 471, 200 ⋅1 7.25 x = 471, 200 x » 64,993.10 The salary is $64,993.10 U.S (0.75) = 0.75 ⋅ 0.75 = 0.5625 X = 70 = 10 51 = 11 190 = 12 123 = 12 ⋅12 ⋅12 = 1728 13 (t ⋅ g ) = t g 14 ( S ) = S 3⋅2 = S 15 92 ⋅ 92 = 9( 16 2+ 2) 65 5-3 = 6( ) = 62 63 ổ 3ử 32 17 ỗỗ ữữữ = ỗố ứ 18 = 94 7m m-n = 7( ) 7n 19 ( x ⋅ y ) = x y æY Y3 20 ỗỗ ữữữ = ỗố R ứ R Chapter Equations and Formulas 21 17 - ⋅ = 17 -12 =5 32 (41 + 23 ¸ 2) = (4 + ¸ 2) 1 = ( + 4) 22 ⋅ - = 72 - = 65 = (8) =8 23 ⋅ 42 + = ⋅16 + = 80 + 33 x - ⋅ = 132 - ⋅ = 169 - ⋅ = 83 = 169 - = 161 24 (9.1-1) ⋅13 = 8.1⋅13 = 105.3 2 34 (9 - y ) + y = (9 - 3) + ⋅ 25 191- 53 = 191-125 = 66 2 = (6) + ⋅ = 36 + ⋅ = 36 + 15 26 (14 - 7) - ⋅ = (7) - ⋅ = 49 - ⋅ = 49 - 24 = 51 35 7r ¸ 32 = ⋅ 27 ¸ 32 = 25 27 = 189 ¸ 32 = 189 ¸ 25 ⋅ = 22 ⋅ 23 = = 21 ổsử ổ 42 36 ỗỗ ữữữ - = ỗỗ ữữữ - ỗố ứ ốỗ x ứ = 20 = 7-4 ổ 3ử 28 1-ỗỗ ữữữ = 1- (0.75) ỗố ø =3 = 1- 0.5625 37 = 0.4375 ( y - 7.8)⋅ 3t = (102 - 7.8)⋅ 3(2) = (100 - 7.8)⋅ 3(2) 29 12 ⋅ 752 = 1⋅ 752 123 = 5625 = (92.2) ⋅ 3(2) = 92.2 ⋅ = 553.2 30 17.2 + (5 - ) = 17.2 + (5 - 4) 3 = 17.2 + = 5088.448 + = 5089.448 0 31 (16 - - 7) = (7) =1 2 ỉ12 ỉ12 38 ỗỗ ữữữ r = ỗỗ ữữữ 92 ỗố ứ ốỗ x ứ = ( 4) ⋅ = 16 ⋅ 81 = 1296 43 44 Chapter Equations and Formulas n 39 ( S - 7) ⋅ 9.2 -1 = (13 - 7) ⋅ 9.2 -1 Chapter Review Exercises = (6) ⋅ 9.2 -1 x + 45 = 96 x + 45 - 45 = 96 - 45 Subtract 45 x = 51 r - 36 = 14.7 r - 36 + 36 = 14.7 + 36 Add 36 r = 50.7 8t + 45 = 175.4 8t + 45 - 45 = 175.4 - 45 Subtract 45 8t = 130.4 8t 130.4 Divide by = 8 t = 16.3 4t - = 15 4t - + = 15 + Add 4t = 21 4t 21 Divide by = 4 t =5 = ⋅ 9.2 -1 = 55.2 -1 = 54.2 40 Gr 21⋅ ⋅ - 22 = ⋅ - 22 2 21⋅ 36 = ⋅ - 22 756 = ⋅ - 22 = 378 ⋅ - 22 = 378 ⋅ - = 2646 - = 2642 41 C = 0.17 N + 12 N + 18,900 = 0.17 (420) + 12 (420) + 18,900 = 0.17 (176, 400) + 12 (420) + 18,900 = 29,988 + 5040 + 18, 900 = 53, 928 The daily cost is $53,928 42 P = 0.027 N + 4.50 N - 62, 700 = 0.027 (1860) + 4.50 (1860) - 62,700 s ⋅ = 42 ⋅ Multiply by 6 s = 252 = 0.027 (3, 459,600) + 4.50 (1860) - 62,700 = 93, 409.20 + 8370 - 62,700 = 39, 079.20 The daily profit is $39,079.20 s = 42 6 t 43 M = P (1 + i ) = $4800 (1 + 0.05) 5z = 85 8 5z 8 ⋅ = ⋅ 85 Multiply by ⋅ 5 s = 136 = $4800 (1.05) = $5834.43 The future value is $5834.43 t 44 M = P (1 + i ) 40 = $15,000 (1 + 0.07) 40 = $15,000 (1.07) = $224, 616.87 The future value is $224,616.87 (rounded) m -5 = m - + = + Add m = 14 m ⋅ = 14 ⋅ Multiply by 4 m = 56 Chapter Equations and Formulas 5( x - 3) = 3( x + 4) 12 x -15 = 3x + 12 Distribute x -15 + 15 = x + 12 + 15 Add 15 x = x + 27 x - 3x = 3x - 3x + 27 Subtract x x = 27 x 27 = 2 27 = 13 x= 2 10 Divide by y = y + 28 y - y = y - y + 28 Subtract y y = 28 y 28 Divide by = 4 y=7 0.6 ( y - 3) = 0.1 y 0.6 y -1.8 = 0.1 y Distribute 0.6 y - 0.6 y -1.8 = 0.1 y - 0.6 y Subtract 0.6 y -1.8 = -0.5 y -1.8 -0.5 y = -0.5 -0.5 Divide by - 0.5 3.6 = y 13 Ninety-four times a number 94 x 14 One half times a number x 15 Six times a number is added to the number 6x + x 3r - = (4 - 3r ) 3r - = - 6r Distribute 3r - + = + - 6r Add 3r = 15 - 6r 3r + 6r = 15 - 6r + 6r Add 6r 9r = 15 9r 15 Divide by = 9 15 x = =1 =1 9 11 45 0.15 (2 x - 3) = 5.85 0.3 x - 0.45 = 5.85 Distribute 0.3 x - 0.45 + 0.45 = 5.85 + 0.45 Add 0.45 0.3 x = 6.3 0.3 x 6.3 = 0.3 0.3 Divide by 0.3 x = 21 16 Five times a number is decreased by 11 x -11 17 The sum of times a number and 3x + 18 (3´$14.95) + $95 = $139.85 Molly purchases will cost $139.85 $139.85 - $47.50 = $92.35 The additional amount she needs is $92.35 19 P = 18.5 A + 4.5 60 = 18.5 A + 4.5 55.5 = 18.5 A 3= A She must spend $3000 on advertising 20 a = amount of water bill 4a = amount of phone bill water bill + phone bill = total + 4a = 540 a Solve the equation a + 4a = 540 5a = 540 a = 108 4a = 432 The water bill is $108 The phone bill is $432 46 Chapter Equations and Formulas 21 n = number of employees more than employees = 24 + ´ n = 24 Solve the equation + n = 24 n = 19 4 ⋅ n = ⋅19 n = 76 The company has 76 employees 22 n 25 M = P (1 + i ) ; M = $14,526.80, i = 0.1, n = 6 $14,526.80 = P (1 + 0.1) $14,526.80 = P (1.1) $14,526.80 = P (1.771561) $14,526.80 1.771561P = 1.771561 1.771561 $8200 » P 26 n = number of children's tickets 100 - n = number of adult tickets children's + $6´ n adult = total sales + $12 (100 - n) = $780 Solve the equation $6n + $12 (100 - n) = $780 $6n + $1200 - $12n = $780 -$6n + $1200 = $780 -$6n = -$420 n = 70 100 - n = 100 - 70 = 30 There were 70 child tickets sold There were 30 adult tickets sold 23 I = PRT ; I = $960, R = 0.12, T = $960 = P ´0.12´ $960 = 0.24 P $960 0.24 P = 0.24 0.24 $ 4000 = P 24 M = P (1 + RT ); M = $3770, R = 0.04, T = $3770 = P (1 + 0.04´ 4) $3770 = P (1 + 0.16) $3770 = P (1.16) $3770 1.16 P = 1.16 1.16 $3250 = P 27 I = PRT ; for R I PRT Divide by PT = PT PT I =R PT M = P (1 + RT ); for T M = P + PRT Distribute M - P = PRT Subtract P M - P PRT Divide by PR = PR PR M -P =T PR 28 B = PR; for P B PR Divide by PR = R R B =P R 29 $17 to 50 cents $17 = 1700 cents 1700 34 = 50 30 days to 12 hours days = 216 hours 216 18 = 12 31 $5000 to $250 5000 20 = 250 32 years to 15 months years = 36 months 36 12 = 15 Chapter Equations and Formulas 33 $2 to 75 cents $2 = 200 cents 200 = 75 34 35 27 v = 14 126 v ⋅126 = 14 ⋅ 27 126v = 378 126v 378 = 126 126 v=3 20 = y 27 ⋅ 27 = y ⋅ 20 135 = 20 y 135 20 y = 20 20 =y z = 12 ⋅12 = ⋅ z 36 = z 36 z = 8 =z 90 37 = 11 t ⋅ t = 11⋅ 90 6t = 990 6t 990 = 6 t = 165 36 20 60 38 = 72 r 20 ⋅ 72 = r ⋅ 60 1440 = 60r 1440 60r = 60 60 24 = r 47 39 x = number of bass with parasites Set up and solve a proportion 14 x = 60 18, 400 14 ⋅18, 400 = 60 ⋅ x 257, 600 = 60 x 4293 » x Approximately 4293 bass have parasites 40 x = pressure at the 9850-foot depth Set up and solve a proportion 3220 6700 = 9850 x 3220 ⋅ 9850 = x ⋅ 6700 31, 717, 000 = 6700 x 4734 » x There is approximately 4734 lb per square inch of pressure at the 9850-foot depth 41 x = total amount of beef needed Set up and solve a proportion 5760 120 = 138 x 5760 ⋅138 = x ⋅120 794,880 = 120 x 6624 = x 6624 pounds of beef are needed for 138 inhabitants 42 x = number of pages proofread in hours hours = 180 minutes Set up and solve a proportion x = 12 180 ⋅180 = 12 ⋅ x 1260 = 12 x 105 = x John proofreads 105 pages in hours 43 x = new quarterly pension required 83 + 21 = 104 total employees Set up and solve a proportion 89,391 83 = 104 x 89,391⋅104 = x ⋅ 83 9, 296, 664 = 83x 112, 008 = x The new quarterly pension contribution required is $112,008 48 Chapter Equations and Formulas 44 x = cost of five shirts Set up and solve a proportion $223.20 = x ⋅ x = ⋅ $223.20 x = $1116 x = $139.50 Five shirts would cost $139.50 0 59 (16 - ⋅ 2) = (16 -16) = (0) (0) is undefined 60 (51 + 23 - 2) = (5 + - 2) 1 = (11) = 11 45 y ⋅ y ⋅ y = y 2 61 ( y - 9) + y = (50 - 9) + ⋅ 50 46 ⋅ = = (41) + ⋅ 50 47 ´ ´ ´ = = 1681 + ⋅ 50 = 1681 + 250 48 3.1⋅ 3.1 = 3.12 = 1931 ỉ1ư 13 49 ỗỗ ữữữ = = ỗố ứ 62 x ¸ 32 = (27) ¸ 32 = (729) ¸ 50 s = 40 = = 2916 ¸ = 324 51 102 = 102 63 P = 1.85 N + 535.20 N - 862, 700 52 00 is undefined 53 72 ⋅ 73 = 7( 2+3) = 1.85(780) + 535.20 (780) - 862, 700 = 1.85(608, 400) + 535.20 (780) - 862,700 = 75 = 1,125,540 + 417, 456 - 862,700 54 ( r ) = r 3⋅2 = r = 680, 296 The total weekly profit is $680,296 55 ( s ⋅ t ) = s 4t t 64 M = P (1 + i ) 25 = $93, 200 (1 + 0.065) ổzử z2 56 ỗỗ ữữữ = ỗố y ứữ y 25 = $93, 200 (1.065) 57 75 - 42 ⋅ = 75 -16 ⋅ = 75 - 32 = 43 58 (1 + 23 ) ¸ = (1 + 8) ¸ 2 = ( 9) ¸ = 81 ¸ = 27 = $449,941.56 The future value is $449,941.56 Chapter Equations and Formulas Business Application Case #1 Breakeven in Retail (a) $8500 + $2100 + $350 + $1620 = $12,570 The total monthly expenses are $12,570 (b) 1- = 10 10 of the revenue remains 10 (c) N = number of books sold in a month gross revenue = ´ revenue 10 net profit = gross revenue - monthly expenses æ3 = ỗỗ $24.80 N ữữữ P $12,570 çè10 ø ỉ3 P = çç ⋅ $24.80 ⋅ N ữữữ - $12,570 ỗố10 ứ P = $7.44 N - $12,570 (d) The break even point occurs when P = P = $7.44 N - $12,570 $0 = $7.44 N - $12,570 $12,570 = $7.44 N 1690 » N The store must sell 1690 books to break even (e) The owner would probably receive a lower salary (f) P = $7.44 N - $12,570 $6000 = $7.44 N - $12,570 $18,570 = $7.44 N 2496 » N The store must sell 2496 books to reach a profit of $6000 49 Business Application Case #2 Expanding the Number of Stores (a) $25 billion 31,000 $25,000, 000,000 = 31,000 » $806, 452 The average sales per store are $806,452 (b) If they add N restaurants next year, the total revenue will be $806, 452 (31,000 + N ) (c) N = ´ 31,000 = 6200 6200 restaurants will be added $806, 452´(31,000 + N ) = $806, 452 ´(31,000 + 6200) = $806, 452 ´37, 200 » $30 billion The estimated revenue will be $30 billion (d) Answers will vary ... biscuits for 125 people Set up and solve a proportion 125 = x ⋅ x = ⋅125 x = 250 x » 36 Approximately 36 cups of flour are needed for biscuits to feed a church group of 125 Chapter Equations and Formulas... = P (1 + RT ); for R Distribute Subtract P Divide by PT P = M (1- DT ); for D P = M - MDT P - M = -MDT P - M -MDT = -MT -MT M -P =D MT I = PRT ; for R I PRT = PT PT I =R PT A ; for i 1+ i A P... B ) h; for h 2 ⋅ A = ⋅ (b + B ) h Multiply by 2 A = (b + B ) h (b + B ) h 2A = (b + B ) (b + B) 37 Use the formula S = 280 + 0.05 x, where x is the employee’s total sales for the week and S is
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