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Solution Manual for Mathematics for the Trades: A Guided Approach, 11th Edition

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    S OLUTIONS M ANUAL H AL M. S AUNDERS M ATHEMATICS FOR THE T RADES A G UIDED A PPROACH Hal M. Saunders Robert A. Carman

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    iii Contents Odd-Numbered Solutions 1 1 Arithmetic of Whole Numbers 3 2 Fractions 17 3 Decimal Numbers 29 4 Ratio, Proportion, and Percent 51 5 Measurement 71 6 Pre-Algebra 91 7 Basic Algebra 101 8 Practical Plane Geometry 129 9 Solid Figures 149 10 Triangle Trigonometry 171 11 Intermediate Algebra 189 12 Statistics 205 Even-Numbered Solutions 229 1 Arithmetic of Whole Numbers 231 2 Fractions 243 3 Decimal Numbers 255 4 Ratio, Proportion, and Percent 277 5 Measurement 301 6 Pre-Algebra 321 7 Basic Algebra 331 8 Practical Plane Geometry 359 9 Solid Figures 377 10 Triangle Trigonometry 399 11 Intermediate Algebra 417 12 Statistics 433

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    Solutions to Odd-Numbered Problems

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    3 CHAPTER 1 ARITHMETIC OF WHOLE NUMBERS Preview 1 1. (a) Two hundred fifty thousand, three hundred seventy-four (b) 1,065,008 3. (a) 67 + 58 = 125 (b) 7009 + 1598 = 8607 5. (a) 64  37 448 192 2368 (b) 305  243 915 1220 610 74115 or 74,115 (c) 908  705 4540 63560 640140 or 640,010 7. (a) 1, 2, 3, 4, 6 and 12 (b) 12 12 2 2 3    2 6 2 3 9. 680 – 235 = 455 lb finished weight Exercises 1-1 Reading, Writing, Rounding, and Adding Whole Numbers A. 1. Three hundred fifty-seven 3. Seventeen thousand, ninety-two 5. Two million, thirty-four 7. Seven hundred forty thousand, one hundred six 9. One hundred eighteen million, one hundred eighty thousand, eighteen 11. 3006 13. 11,100 15. 4,040,006 17. 360 19. 4000 21. 230,000 B. 1. 69 3. 80 5. 123 7. 132 9. 806 11. 1390 13. 1009 15. 861 17. 5461 19. 11,428 21. 11,071 23. 25,717 25. 175,728 27. 6095 29. 663,264

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    4 Mathematics for the Trades , 11e C. 1. 1042 3. 6352 5. 6514 7. 2442 9. 7083 11. 4114 13. 64 15. 55 17. 55 19. 1,166,040 D. 1. 387 913 76 2640 + 845 4861 ft 3. 346 275 84 128 325 98 260 + 120 1636 screws 5. 78 428 143 96 + 384 1129 minutes 7. (a) 420 260 875 340 558 564 280 + 310 3607 watts (b) 875 564 + 558 1997 watts (c) 260 280 + 310 850 watts 9. 1205 865 742 + 257 3114 bricks 11. $ 599 309 369 + 280 $ 1557 13. 520 1160 49 + 1200 2929 ohms 15. 485 74 251 + 146 756 grams 17. 1400 1800 600 + 100 3900 W 19. (a) 1172 1054 915 + 1123 4264 points (b) 1264 776 + 987 3027 points (c) 4264 + 3027 7291 points

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    Chapter 1 Arithmetic of Whole Numbers 5 E. 1. 35,244 + 61,775 97,001 kHz 3. (a) $307,225 (b) $732,813 (c) $2,298,502 (d) $7156 5. (a) Total feet of each kind 11,453 ft of #12 BHD 258 ft of #TX 12,715 ft of 410 AAC 8792 ft of 110 ACSR 7425 ft of 6B (b) Total feet installed at each location 3530 ft at A3 8412 ft at A4 4294 ft at B1 5482 ft at B5 5073 ft at B6 6073 ft at C4 7779 ft at C5 Exercises 1-2 Subtraction of Whole Numbers A. 1. 35 3. 25 5. 33 7. 62 9. 13 11. 12 13. 15 15. 38 17. 46 19. 25 21. 189 23. 281 25. 408 27. 273 29. 574 31. 2809 33. 12,518 35. 4741 37. 47,593 B. 1. $ 486 27 $ 459  3. 3540 1782 17 t ft 58 f  5. $ 1206512 – 875977 $ 330535 or $330,535 7. The 4 drums contain 72 + 45 + 39 + 86 = 242 liters 3 drums contain 97 + 115 + 74 = 286 liters The total volume of the 3 drums is greater by (286 – 242) = 44 liters. 9. 238 64 174 gal    11. 22,000 – 14,250 7,750 impressions 13. 20000 – 6500 13500 ohms or 13,500 ohms 15. 1350000  850000 500000 Hertz or 500,000 Hertz 17. 8823 – 8701 122 HCF

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    6 Mathematics for the Trades , 11e 19. Hyundai Sonata: $ 28185 5444 8166 + 4716 $ 46511 – 9419 $ 37092 or $37,092 Sonata Hybrid: $ 30935 3953 9101 + 4168 $ 48157 – 9107 $ 39050 or $39,050 Therefore, the Sonata costs less than the Sonata Hybrid by $1958. C. 1. Total mileage of each # 1 60,027 – 58,352 = 1675 # 2 43,302 – 42,135 = 1167 # 3 78,007 – 76,270 = 1737 # 4 41,322 – 40,006 = 1316 # 5 10,002 – 08,642 = 1360 # 6 35,700 – 35,401 = 299 # 7 80,101 – 79,002 = 1099 # 8 40,122 – 39,987 = 135 # 9 11,671 – 10,210 = 1461 #10 73,121 – 71,040 = 2081 Total mileage of all = 12330 or 12,330 3. $ 28245 – 3814 $2 4 4 31 or 24,431 5. (a) Balance A = $2065 (b) $ 6375 6375  379 = 5996 5996 + 1683 = 7679 7679 + 474 = 8153 8153 + 487 = 8640 8640  2373 = 6267 6267  1990 = 4277 4277  308 = 3969 3969  1090 = 2879 2879  814 = 2065 Exercises 1-3 Multiplication of Whole Numbers A. 1. 42 3. 48 5. 63 7. 54 9. 45 11. 296 13. 576 15. 320 17. 290 19. 282 21. 416 23. 792 25. 1404 27. 720 29. 5040 31. 1938 33. 4484 35. 3822

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    Chapter 1 Arithmetic of Whole Numbers 7 B. 1. 809  9 7281 3. 8043  37 56301 24129 297591 or 297,591 5. 500  50 25000 or 25,000 7. 316  32 632 948 10112 or 10,112 9. 684  45 3420 2736 30780 or 30,780 11. 305  123 915 610 305 37515 or 37,515 13. 807  111 807 807 807 89577 or 89,577 15. 7009  504 28036 350450 3532536 or 3,532,536 17. 3706  102 7412 37060 378012 or 378,012 19. 2008  198 16064 18072 2008 397584 or 397,584 C. 1. $ 75  40 $ 3000 3. 65  20 1300 ft 5. 50  18 400 50 900 100  16 1600 500  11 500 500 5500 900 1600 + 5500 8000 = total envelopes 7. 27  2 54  45 270 216 2430 parts 9. 60  4 240  5 1200 bolts 11. 850  9 7650 cards 13. 60 1440  24  16 240 8640 120 1440 1440 min 23040 screws or 23,040 screws 15. 23  5 115 in. (or 9 ft 7 in.) 17. 850  25 4250 1700 21250 ohms or 21,250 ohms, No 19. 170  220 000 340 340 37400 bu or 37,400 bu 21. 96  5 480 A

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    8 Mathematics for the Trades , 11e 23. 176  500 000 000 880 88000 mL or 88,000 mL 25. $ 16  40 00 64 $ 640 $ 640  52 1280 3200 $ 33280 or $33,280 27. 250  60 000 1500 15000 gal/hr or 15,000 gal/hr 15000  2 30000 gal or 30,000 gal 29. 800  170 000 5600 800 136000 or 136,000 lb D. 1. $873  365 = $318,645 $1,000,000 – 318,645 = $681,355 3. (a) 111,111,111 222,222,222 333,333,333 (b) 111,111 222,222 333,333 (c) 1 121 12,321 1,234,321 123,454,321 (d) 42 4422 444,222 44,442,222 4,444,422,222 5. 8 hours/day  5 days/week = 40 hours/week Alpha 117  $ 6  40 = $ 28,080 Beta 67  $17  40 = $ 45,560 Gamma 29  $32  40 = $ 37,120 Delta 37  $49  40 = $ 72,520 Tau 18  $78  40 = $ 56,160 Exercises 1-4 Division of Whole Numbers A. 1. 9 7 63 63 3. 8 4 32 32 5. 6 9 54 54 7. 14 r2 5 72 5 22 20 2

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    Chapter 1 Arithmetic of Whole Numbers 9 9. 10 r1 7 71 7 01 0 1 11. 23 r6 7 167 14 27 21 6 13. 51 r4 6 310 30 10 6 4 15. 210 r6 9 1476 14 07 7 06 0 6 17. 37 6 222 18 42 42 19. 222 r2 9 2000 18 20 18 20 18 2 21. 501 7 3507 35 007 7 23. 24 604 6 3624 36 024 24 B. 1. 23 14 322 28 42 42 3. 39 24 936 72 216 216 5. 9 r1 81 730 729 1 7. 2 22 31 682 62 62 62 9. 8 r35 42 371 336 35 11. 120 61 7320 61 122 122 20 0 0 13. 56 r8 16 904 80 104 96 8 15. 305 r5 14 4275 42 075 70 5 17. 119 53 6307 53 100 53 477 477 19. 96 21 2016 189 126 126 21. 0 200 15 3000 30 000 0 23. 108 r4 24 2596 24 196 192 4 96 25. 600 38 22800 228 000 27. 102 r98 411 42020 411 920 822 98 29. 17 r123 405 7008 405 2958 2835 123 8 C. 1. (a) 1, 2, 3, 6 (b) 6 = 2  3 3. (a) 1, 19 (b) prime 5. (a) 1, 2, 4, 5, 8, 10, 20, 40 (b) 40 = 2  2  2  5

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    10 Mathematics for the Trades , 11e D. 1. 27 in. 9 243 18 63 63 3 3. 13 hr 85 1105 85 255 255 5 5. 27 1 28 joists 16 432 32 11 2 2 2 11   7. 7 in. 18 126 126 9. $ 4696 – 3400 $ 1296 $72 per hour 18 1296 126 36 36 6 11. 48 boxes 10 480 40 80 80 0 13. 27 reams 500 13500 1000 3500 3500 0 15. 6 loops 3 18 17. 230 months 30 6900 60 90 9 0 0 0 0 00 0 19 12 230 12 110 108 2 0 19 years, 2 months 19. 00 0 250 minutes 200 50000 400 1000 10 0 0 0 00 4 60 250 240 10 4 hr, 10 min 21. 21 eight-foot lengths 8 168 168 8 8 21  $ 22 42 42 $ 462

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    Chapter 1 Arithmetic of Whole Numbers 11 E. 1. (a) 4464  48 = 93 (b) 169,722  378 = 449 3. 6587  344 = 19.148... or 20 rivets to be sure 5. 297,600  96 = 3100 min 3100  60 = 51.666... or 51 hr 40 min 7. 42 115 4830 460 230 230 Exercises 1-5 Order of Operations A. 1. 2 + 8  6 = 2 + 48 = 50 3. 40  20  5 = 40  4 = 36 5. 16  3 + 9 = 48 + 9 = 57 7. 48  8  2 = 6  2 = 4 9. (5 + 9)  3 = 14  3 = 42 11. 24  (6  2) = 24  4 = 6 13. 16 + 5  (3 + 6) = 16 + 5  9 = 16 + 45 = 61 15. (23 + 5)  (12  8) = 28  4 = 112 17. 6 + 4  7  3 = 6 + 28  3 = 34  3 = 31 19. 5  8 + 6  6  12  2 = 40 + 1  24 = 41  24 = 17 21. 2  (6 + 4  9) = 2  (6 + 36) = 2  42 = 84 23. (4  3 + 8)  5 = (12 + 8)  5 = 20  5 = 4 25. 8  4 + 2 = 4 + 2 = 6 27. 18  10  5 = 180  5 = 36 29. 12 7 3 5 3 2      31. 12 7 3 1 ( 4 ) 2 8      33. 36 27 4 9 13 9 3     35. 44 12 56 11 3 8    = 7 37. 6 12 4 6 48 54 15 3 2 15 6 9         = 6 39. 12 6 24 6 6 3 6 6       18 9 4 1 2 4 1 6 1 5         hours

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    12 Mathematics for the Trades , 11e B. 1. 3  $34 + 5  $39 = $102 + $195 = $297 3. 12  $30 – 3  $6 = $360 – $18 = $342 5. Cost = 2  $12  40 + 3  $20  40 + $3240 + $500 = $960 + $2400 + $3240 + $500 = $7100 7. 33  $80 + 12  $40 + 45  $18 = $2640 + $480 + $810 = $3930 9. China: 51  5 + 21  3 + 28  1 = 255 + 63 – 28 = 346 points U.S.: 36  5 + 38  3 + 36  1 = 180 + 114 + 36 = 330 points China “won.” 11. 8 gal 22 176 176 0 gal 6 30 180 180 0 8 gal + 6 gal = 14 gal C. 1. 462 + 83  95 = 462 + 7885 = 8347 3. 7482 – 1152  12 = 7482 – 96 = 7386 5. (268 + 527)  159 = 795  159 = 5 7. 612 + 86  9 – 1026  38 = 612 + 774 – 27 = 1359 9. 3579 – 16  (72 + 46) = 3579 – 16  118 = 3579 – 1888 = 1691 11. 864  16  27 = 54  27 = 1458 13. (296 + 18  48)  12 = (296 + 864)  12 = 1160  12 = 13,920 15. (3297 + 1858 – 493)  (48  16 – 694) = 63 Problem Set 1 A. 1. Five hundred ninety-three 3. Forty-five thousand, two hundred six 5. Two million, four hundred three thousand, five hundred sixty 7. Ten thousand twenty

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    Chapter 1 Arithmetic of Whole Numbers 13 9. Twelve billion, six hundred four million, seven hundred thousand, two hundred fifty 11. 230,056 13. 64,700 15. 6,047,920,000 17. 5500 19. 94,700 21. 710,000 B. 1. 87 + 9 96 3. 63 – 8 55 5. 24 + 69 93 7. 456 + 72 528 9. 396 + 538 934 11. 43 – 28 15 13. 734 – 85 649 15. 543 – 348 195 17. 376  4 1504 19. 67  21 67 134 1407 21. 207  63 621 1242 13041 or 13,041 23. 5236  44 20944 20944 230384 or 230,384 25. 9 37 7 259 21 49 49 27. 4 57 42 2394 210 294 294 29. 9 160 1440 1440 31. 0 4 18 73 1314 73 584 584 33. 36 91 13 42   = 3276 546 6 546 3276 3276  36  91 36 324 3276 42  13 126 42 546 35. 120 – 40  8 = 120 – 5 = 115 37. 3  4 – 15  3 = 12 – 5 = 7 39. 308 793 144 1245 41. 256 965 89 42 1352 C. 1. (a) 1, 2, 4, 8, (b) 8 = 2  2  2 3. (a) 1, 31 (b) prime 5. (a) 1, 2, 3, 4, 6, 9, 12, 18, 36 (b) 36 = 2  2  3  3

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    14 Mathematics for the Trades , 11e D. 1. 6 ft + 8 ft + 20 ft + 9 ft = 43 ft 3. (a) 40 26 14 ft; x    15 12 27 ft y    (b) 54 22 14 18 ft; x     31 19 50 ft y    5. 6 35 210 210 7. 210 215 245 217 220 227 115 1449 207 lb average 7 4 1449 14 49 9 49 9. $400 + 12  $110 = $400 + $1320 = $1720 $ 110  12 220 110 $1320 11. 136  107 29 psi, Yes 13. 6000 000 0 39000 gal per hour 4 156000 12 00 36 36 650 gal per min 60 39000 360 300 30 0 0 00 0 15. 167  17 = 2839 lb 17. 3 4  32 = 24 hours Note: 45 min = 3 4 hr 19. 380  231 380 11400 760 87780 or 87,780 cu in. 21. 506409 – 460089 46320 or 46,320 in 4 hr 11580 rph 4 46320 193 rpm 60 11580 60 558 540 180 180 0 80 0 0 23. 18 – 6 12 12  2 = 6 ft from each wall

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