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Solution Manual for Basic College Mathematics, 13th Edition

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     S OLUTIONS M ANUAL B ASIC C OLLEGE M ATHEMATICS T HIRTEENTH E DITION Marvin L. Bittinger Indiana University Purdue University Indianapolis Judith A. Beecher Barbara L. Johnson Ivy Tech Community College of Indiana

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    Contents Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . 43 Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . 71 Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . . . 95 Chapter 6 . . . . . . . . . . . . . . . . . . . . . . . . . 115 Chapter 7 . . . . . . . . . . . . . . . . . . . . . . . . . 139 Chapter 8 . . . . . . . . . . . . . . . . . . . . . . . . . 157 Chapter 9 . . . . . . . . . . . . . . . . . . . . . . . . . 179 Chapter 10 . . . . . . . . . . . . . . . . . . . . . . . . . 199 Chapter 11 . . . . . . . . . . . . . . . . . . . . . . . . . 213

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    Chapter 1 Whole Numbers Exercise Set 1.1 RC2. In 615,702, the number 615 is in the thousands period. RC4. The number 721 is written in standard notation. CC2. A word name for 42,000,000 is forty-two million. CC4. A word name for 18,000,000,000 is eighteen billion. CC6. A word name for 40,000,000,000,000 is forty trillion. 2. 5 ten thousands 4. 5 hundred thousands 6. 9 8. 3 10. 6 thousands + 6 hundreds + 8 tens + 8 ones 12. 1 thousand + 7 hundreds + 8 tens + 6 ones 14. 3 ten thousands + 8 thousands + 4 hundreds + 5 tens + 3 ones 16. 1 hundred thousand + 3 ten thousands + 5 thousands + 0 hundreds + 8 tens + 0 ones, or 1 hundred thousand + 3 ten thousands + 5 thousands + 8 tens 18. 1 bil l ion + 2 h undred millions + 6 ten millions + 6 millions + 8 hundred thousands + 8 ten thousands + 3 thousands + 5 hundreds + 9 tens + 8 ones 20. 3 hundred millions + 2 ten millions + 3 millions + 9 hun- dred thousands + 9 ten thousands + 5 thousands + 5 hundreds + 2 tens + 8 ones 22. Forty-eight 24. Forty-five thousand, nine hundred eighty-seven 26. One hundred eleven thousand, thirteen 28. Forty-three billion, five hundred fifty million, six hundred fifty-one thousand, eight hundred eight 30. Ninety-nine thousand, eight hundred fifty-three 32. Two hundred twenty-six million, one thousand, two hun- dred eighty-eight 34. 354,702 36. 17,112 38. 19,610,439 40. 700,000,000 42. 26,000,000,000 44. 200,017 46. 2,793,000,000 48. All digits are 9’s. Answers may vary. For an 8-digit read- out, for example, it would be 99,999,999. This number has three periods. Exercise Set 1.2 RC2. In the addition 5 + 2 = 7, the number 7 is the sum. RC4. The distance around an object is its perimeter. CC2. 110 CC4. 1700 CC6. 10,000 2. 1 5 2 1 + 3 4 8 1 8 6 9 4. 1 7 3 + 6 9 1 4 2 6. 1 7 5 0 3 + 2 6 8 3 1 0 , 1 8 6 8. 1 1 9 9 9 + 1 1 1 0 1 0 10. 1 2 7 1 + 3 3 3 8 3 6 0 9 12. 1 2 8 0 + 3 4 , 9 0 2 3 5 , 1 8 2 14. 1 1 1 1 0 , 1 2 0 1 2 , 9 8 9 + 5 7 3 8 2 8 , 8 4 7 16. 1 3 6 5 4 + 2 7 0 0 6 3 5 4 18. 1 1 1 4 5 , 8 7 9 + 2 1 , 7 8 6 6 7 , 6 6 5

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    2 Chapter 1: Whole Numbers 20. 1 1 1 1 9 9 , 9 9 9 + 1 1 2 1 0 0 , 1 1 1 22. 2 3 8 2 7 3 2 1 4 + 7 6 1 8 7 24. 1 1 1 1 4 2 , 4 8 7 8 3 , 1 4 1 + 3 6 , 7 1 2 1 6 2 , 3 4 0 26. 2 2 9 8 9 5 6 6 8 3 4 9 2 0 + 7 0 3 4 0 1 2 28. Perimeter = 14 mi + 13 mi + 8 mi + 10 mi + 47 mi + 22 mi We carry out the addition. 2 1 4 1 3 8 1 0 4 7 + 2 2 1 1 4 The perimeter of the figure is 114 mi. 30. Perimeter = 62 yd + 39 yd + 54 yd + 46 yd + 28 yd We carry out the addition. 2 6 2 3 9 5 4 4 6 + 2 8 2 2 9 The perimeter of the figure is 229 yd. 32. 90 ft + 90 ft + 90 ft + 90 ft = Perimeter We carry out the addition. 9 0 9 0 9 0 + 9 0 3 6 0 The batter travels 360 ft when a home run is hit. 34. Nine billion, three hundred forty-six million, three hundred ninety-nine thousand, four hundred sixty-eight Exercise Set 1.3 RC2. subtraction symbol RC4. difference CC2. 9 10 1 0 0 / ✥✥ − 7 9 3 CC4. 10 1 / 0 / 0 0 − 4 0 0 6 0 0 CC6. 9 9 10 1 0 0 0 / ✥✥✥ − 9 9 9 1 2. 8 7 − 3 4 5 3 4. 5 2 6 − 3 2 3 2 0 3 6. 6 13 7 / 3 / − 2 8 4 5 8. 5 14 6 / 4 / − 1 9 4 5 10. 18 6 8 / 15 7 / 9 / 5 / − 3 9 8 3 9 7 12. 10 2 0 / 16 3 / 1 / 6 / − 2 4 7 6 9 14. 17 7 7 / 17 8 / 8 / 7 / − 6 9 8 1 8 9 16. 3 12 3 4 / 2 / − 2 1 7 1 2 5

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    Exercise Set 1.4 3 18. 13 12 5 3 / 2 / 11 6 / 4 / 3 / 1 / − 2 8 9 6 3 5 3 5 20. 12 15 7 2 / 5 / 14 8 / 3 / 6 / 4 / − 5 3 7 5 2 9 8 9 22. 11 13 8 1 / 3 / 11 9 / 2 / 4 / 1 / − 5 6 4 3 3 5 9 8 24. 6 15 7 / 5 / 8 3 − 3 6 4 1 3 9 4 2 26. 11 11 5 1 / 1 / 12 1 6 / , 2 / 2 / 2 / − 5 , 8 8 8 1 0 , 3 3 4 28. 11 2 1 / 11 8 14 3 / 2 / , 1 / 9 / 4 / − 2 9 , 2 3 6 2 9 5 8 30. 8 10 9 / 0 / − 7 8 1 2 32. 7 9 13 8 0 3 ✥✥ − 4 1 8 3 8 5 34. 3 9 15 9 4 0 5 / ✥✥ − 2 5 8 9 1 4 7 36. 14 6 4 / 9 10 7 / 5 0 0 / ✥✥ − 3 6 0 4 3 8 9 6 38. 6 9 13 8 4 , 7 0 3 / ✥✥ − 2 9 8 8 4 , 4 0 5 40. 14 4 / 10 0 17 1 / 5 / , 0 / 1 / 7 / − 7 8 0 9 7 2 0 8 42. 7 9 9 13 8 0 0 3 / ✥✥✥ − 5 9 9 7 4 0 4 44. 6 9 9 10 1 7 , 0 0 0 / ✥✥✥ − 1 1 , 5 9 8 5 4 0 2 46. 3 9 9 9 16 4 0 , 0 0 6 / ✭✭✭✭ − 1 4 7 3 9 , 8 5 9 48. 2 9 9 9 14 3 0 , 0 0 4 / ✭✭✭✭ − 6 7 4 9 2 3 , 2 5 5 50. 9 0 1 + 2 3 9 2 4 52. 1 9 9 0 9 + 1 0 1 1 1 0 , 9 2 0 54. 9 thousands + 1 hundred + 0 tens + 3 ones, or 9 thousands + 1 hundred + 3 ones 56. 3 , 928 , 124 − 1 , 098 , 947 Using a calculator to carry out the subtraction, we find that the difference is 2,829,177. Exercise Set 1.4 RC2. In the multiplication 4 × 3 = 12, 12 is the product. RC4. The product of 1 and any number a is a . CC2. 4800 CC4. 80,000 CC6. 400,000 2. 2 8 7 × 4 3 4 8 4. 5 7 6 × 9 6 8 4 6. 4 8 0 6 × 7 5 6 4 2 8. 3 2 2 7 8 6 7 × 4 3 1 , 4 6 8

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    4 Chapter 1: Whole Numbers 10. 4 7 8 × 6 0 4 6 8 0 12. 2 2 8 7 × 3 4 3 4 8 2 6 1 0 2 9 5 8 14. 2 3 4 0 × 1 0 0 0 2 , 3 4 0 , 0 0 0 16. 8 0 0 × 7 0 0 5 6 0 , 0 0 0 18. 5 4 5 4 7 7 7 × 7 7 5 4 3 9 5 4 3 9 0 5 9 , 8 2 9 20. 3 7 3 7 5 4 9 × 8 8 4 3 9 2 4 3 9 2 0 4 8 , 3 1 2 22. 2 1 1 1 4 3 2 × 3 7 5 2 1 6 0 3 0 2 4 0 1 2 9 6 0 0 1 6 2 , 0 0 0 24. 2 3 2 3 4 5 3 4 6 × 6 5 9 3 1 1 4 1 7 3 0 0 2 0 7 6 0 0 2 2 8 , 0 1 4 26. 2 2 6 1 5 1 1 8 9 2 8 × 3 1 7 2 1 7 8 5 6 6 2 4 9 6 0 8 9 2 8 0 0 2 6 7 8 4 0 0 0 2 8 , 3 1 9 , 6 1 6 28. 2 4 2 4 1 3 6 4 0 8 × 6 0 6 4 2 5 6 3 2 3 8 4 4 8 0 3 8 4 4 8 0 0 0 3 8 , 8 5 8 , 1 1 2 30. 1 1 4 4 4 4 3 5 5 × 2 9 9 3 1 9 5 3 1 9 5 0 7 1 0 0 0 1 0 6 , 1 4 5 32. 1 2 2 4 1 6 5 2 1 × 3 4 4 9 5 8 6 8 9 2 6 0 8 4 0 2 6 0 8 4 0 0 1 9 5 6 3 0 0 0 2 2 , 4 9 0 , 9 2 9 34. 3 4 4 4 4 5 0 6 × 7 8 0 0 3 6 0 4 8 0 0 3 1 5 4 2 0 0 0 3 5 , 1 4 6 , 8 0 0 36. 1 2 6 0 0 9 × 2 0 0 3 1 8 0 2 7 1 2 0 1 8 0 0 0 1 2 , 0 3 6 , 0 2 7 38. A = l × w = 129 yd × 65 yd = 8385 sq yd 40. A = l × w = 200 ft × 85 ft = 17 , 000 sq ft 42. 1 2 2 9 8 7 6 8 7 6 7 6 + 6 1 0 , 8 3 4 44. 13 2 3 / 10 8 18 3 / 4 / 0 / , 7 9 / 8 / − 8 6 , 6 7 9 2 5 4 , 1 1 9 46. 0

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    Exercise Set 1.5 5 48. Seven million, four hundred thirty-two thousand Exercise Set 1.5 RC2. dividend RC4. divisor CC2. 3 4 1 5 1 2 3 The answer is 3 R 3. CC4. 4 8 2 9 7 8 1 7 1 6 1 The answer is 48 R 1. 2. 54 ÷ 9 = 6 because 54 = 9 · 6. 4. 37 37 = 1 Any nonzero number divided by itself is 1. 6. 56 1 = 56 Any number divided by 1 is that same number. 8. 0 32 = 0 Zero divided by any nonzero number is 0. 10. 74 ÷ 0 is not defined, because division by 0 is not defined. 12. 20 4 = 5 because 20 = 4 · 5. 14. 2 3 3 3 6 9 9 6 9 9 9 9 0 The answer is 233. 16. 1 0 8 8 8 6 9 8 6 9 6 4 5 The answer is 108 R 5. 18. 7 0 8 3 2 1 2 4 2 1 2 4 2 4 0 The answer is 708. 20. 1 0 1 2 9 9 1 1 0 9 1 1 9 2 0 1 8 2 The answer is 1012 R 2. 22. 1 9 4 2 3 8 9 2 1 8 1 8 9 8 1 The answer is 194 R 1. 24. 1 4 6 6 8 8 1 6 2 8 2 4 4 1 3 6 5 The answer is 146 R 5. 26. 2 0 0 9 3 6 0 2 7 6 2 7 2 7 0 The answer is 2009. 28. 5 1 7 8 4 1 3 9 4 0 1 3 8 5 9 5 6 3 The answer is 517 R 3. 30. 1 2 7 0 1 0 0 1 2 7 , 0 0 0 1 0 0 2 7 0 2 0 0 7 0 0 7 0 0 0 0 0 The answer is 1270.

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    6 Chapter 1: Whole Numbers 32. 4 2 6 1 0 4 2 6 0 4 0 2 6 2 0 6 0 6 0 0 The answer is 426. 34. 2 8 9 2 0 5 7 9 8 4 0 1 7 9 1 6 0 1 9 8 1 8 0 1 8 The answer is 289 R 18. 36. 2 4 4 0 9 8 7 8 0 1 8 7 1 6 0 2 7 The answer is 24 R 27. 38. 4 0 2 3 9 4 2 9 2 2 2 The answer is 40 R 22. 40. 5 0 5 4 2 7 2 9 2 7 0 2 9 The answer is 50 R 29. 42. 5 5 1 0 2 5 6 1 2 5 1 0 5 1 2 5 1 0 2 The answer is 55 R 2. 44. 1 0 7 7 7 4 9 7 4 9 4 9 0 The answer is 107. 46. 8 0 8 9 7 2 7 3 7 2 7 3 7 2 1 The answer is 808 R 1. 48. 1 0 1 0 7 7 0 7 4 7 0 7 7 4 The answer is 1010 R 4. 50. 3 0 1 2 4 7 2 4 2 7 2 4 2 2 4 1 8 The answer is 301 R 18. 52. 1 0 2 4 8 4 8 9 9 4 8 9 9 9 6 3 The answer is 102 R 3. 54. 2 1 0 3 6 7 5 6 3 7 2 3 6 3 6 3 The answer is 210 R 3. 56. 8 0 3 3 6 2 8 , 9 2 9 2 8 8 1 2 9 1 0 8 2 1 The answer is 803 R 21. 58. 9 8 4 9 0 8 8 , 5 6 0 8 1 0 7 5 6 7 2 0 3 6 0 3 6 0 0 The answer is 984.

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    Chapter 1 Mid-Chapter Review 7 60. 2 9 0 4 3 0 6 8 8 8 , 8 8 8 6 1 2 2 7 6 8 2 7 5 4 1 4 8 8 1 2 2 4 2 6 4 The answer is 2904 R 264. 62. 7 0 0 2 8 0 3 5 , 6 2 2 , 6 0 6 5 6 2 1 1 6 0 6 1 6 0 6 0 The answer is 7002. 64. 8 8 , 7 7 7 − 2 2 , 3 3 3 6 6 , 4 4 4 66. 2 6 8 × 3 5 1 3 4 0 8 0 4 0 9 3 8 0 68. A = l × w = 11 ft × 9 ft = 99 sq ft 70. Pairs of factors whose product is 36 are: 1 and 36 2 and 18 3 and 12 4 and 9 6 and 6 a) The pair above whose sum is 13 is 4 and 9. b) The pair above whose difference is 0 is 6 and 6. c) The pair above whose sum is 20 is 2 and 18. d) The pair above whose difference is 9 is 3 and 12. 72. 34 , 584 , 132 ÷ 76 = 4 , 386 Consider the related multiplication sentence: 4 , 386 · 76 = 34 , 584 , 132 Since the ones digit of the product is 2, the missing ones digit must be either 2 or 7 (6 · 2 = 12 and 6 · 7 = 42). We try 2: 34 , 584 , 132 ÷ 762 = 45 , 386 We see that the missing ones digit is 2 and the missing thousands digit is 5. Chapter 1 Mid-Chapter Review 1. The statement is false. For example, 8 − 5 = 3, but 5 is not equalto 8 + 3. 2. The statement is true. See page 19 in the text. 3. The statement is true. See page 19 in the text. 4. The statement is false. For example, 3 · 0 = 0 and 0 is not greater than 3. Also, 1 · 1 = 1 and 1 is not greater than 1. 5. It is true that zero divided by any nonzero number is 0. 6. The statement is false. Any number divided by 1 is the number itself. For example, 27 1 = 27. 7. 95 ︸︷︷︸ , 406 ︸︷︷︸ , 237 ︸︷︷︸ ↑ ↑ ↑ Ninety-five million, four hundred six thousand, two hundred thirty-seven 8. 5 9 14 6 0 4 / ✥✥ − 4 9 7 1 0 7 9. 2 6 9 8 The digit 6 names the number of hundreds. 10. 6 1, 2 0 4 The digit 6 names the number of ten thousands. 11. 1 4 6 , 2 3 7 The digit 6 names the number of thousands. 12. 5 8 6 The digit 6 names the number of ones. 13. 3 0 6, 4 5 8, 1 2 9 The digit 2 names the number of tens. 14. 3 0 6 , 4 5 8, 1 2 9 The digit 6 names the number of millions. 15. 3 0 6, 4 5 8, 1 2 9 The digit 5 names the number of ten thousands. 16. 3 0 6, 4 5 8, 1 2 9 The digit 1 names the number of hundreds. 17. 5602 = 5 thousands + 6 hundreds + 0 tens + 2 ones, or 5 thousands + 6 hundreds + 2 ones 18. 69,345 = 6 ten thousands + 9 thousands + 3 hundreds + 4 tens + 5 ones 19. A word name for 136 is one hundred thirty-six. 20. A word name for 64,325 is sixty-four thousand, three hun- dred twenty-five. 21. Standard notation for three hundred eight thousand, seven hundred sixteen is 308,716. 22. Standard notation for four million, five hundred sixty- seven thousand, two hundred ninety-one is 4,567,291.

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    8 Chapter 1: Whole Numbers 23. 3 1 6 + 4 8 2 7 9 8 24. 1 1 5 9 3 + 4 3 7 1 0 3 0 25. 1 1 2 6 3 8 + 5 2 8 4 7 9 2 2 26. 1 1 1 4 6 1 7 2 4 3 6 + 4 8 1 7 5 3 4 27. 7 8 6 − 3 2 1 4 6 5 28. 11 5 1 / 14 6 / 2 / 4 / − 2 8 5 3 3 9 29. 15 2 5 / 9 12 3 / 6 0 2 / ✥✥ − 1 7 4 8 1 8 5 4 30. 4 9 9 14 5 0 0 4 / ✥✥✥ − 6 7 6 4 3 2 8 31. 3 3 6 × 6 2 1 6 32. 1 1 5 5 5 6 7 × 2 8 4 5 3 6 1 1 3 4 0 1 5 , 8 7 6 33. 2 1 3 4 0 7 × 3 2 5 2 0 3 5 8 1 4 0 1 2 2 1 0 0 1 3 2 , 2 7 5 34. 2 2 3 1 9 4 3 5 × 6 0 2 1 8 8 7 0 5 6 6 1 0 0 0 5 , 6 7 9 , 8 7 0 35. 2 5 3 4 1 0 1 2 8 2 1 2 0 1 2 1 2 0 The answer is 253. 36. 1 1 2 3 8 4 2 6 1 3 8 4 6 3 8 8 1 7 6 5 The answer is 112 R 5. 37. 2 3 6 0 1 3 9 9 1 2 0 1 9 9 1 8 0 1 9 The answer is 23 R 19. 38. 1 4 4 5 6 8 0 9 5 5 6 2 4 9 2 2 4 2 5 5 2 2 4 3 1 The answer is 144 R 31. 39. Perimeter = 10 m + 4 m + 8 m + 3 m = 25 m 40. A = 4 in. × 2 in. = 8 sq in. 41. When numbers are being added, it does not matter how they are grouped. 42. Subtraction is not commutative. For example, 5 − 2 = 3, but 2 − 5  = 3. 43. Answers will vary. Suppose one coat costs $150. Then the multiplication 4 · $150 gives the cost of four coats. Suppose one ream of copy paper costs $4. Then the mul- tiplication $4 · 150 gives the cost of 150 reams. 44. Using the definition of division, 0 ÷ 0 = a such that a · 0 = 0. We see that a could be any number since a · 0 = 0 for any number a . Thus, we cannot say that 0 ÷ 0 = 0. This is why we agree not to allow division by 0.

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    Exercise Set 1.6 9 Exercise Set 1.6 RC2. Because the digit in the hundreds place, 5, is 5 or higher, we round up. The statement is false. RC4. The statement is true. See page 40 in the text. CC2. 1000 2. 530 4. 8950 6. 50 8. 800 10. 900 12. 700 14. 4600 16. 198,400 18. 5000 20. 2000 22. 736,000 24. 6,713,000 26. 6 2 6 0 9 7 1 0 0 4 6 5 0 + 8 1 + 8 0 2 9 0 28. 6 7 3 6 7 0 − 2 8 − 3 0 6 4 0 30. 4 1 4 0 2 1 2 0 5 5 6 0 + 6 0 + 6 0 1 7 7 1 8 0 32. 8 3 6 8 4 0 3 7 4 3 7 0 7 9 4 7 9 0 + 9 3 8 + 9 4 0 3 9 4 7 2 9 4 0 3947 seems to be incorrect. 34. 5 6 8 6 0 0 4 7 2 5 0 0 9 3 8 9 0 0 + 4 0 2 + 4 0 0 2 4 0 0 36. 9 4 3 8 9 4 0 0 − 2 7 8 7 − 2 8 0 0 6 6 0 0 38. 4 8 1 5 0 0 7 0 2 7 0 0 6 2 3 6 0 0 + 1 0 4 3 + 1 0 0 0 1 8 4 9 2 8 0 0 1849 seems to be incorrect. 40. 3 2 6 3 0 0 2 7 5 3 0 0 7 5 8 8 0 0 + 9 4 3 + 9 0 0 2 3 0 2 2 3 0 0 42. 7 6 4 8 8 0 0 0 9 3 4 8 9 0 0 0 7 8 4 2 8 0 0 0 + 2 2 2 2 + 2 0 0 0 2 7, 0 0 0 44. 8 4, 8 9 0 8 5, 0 0 0 − 1 1, 1 1 0 − 1 1, 0 0 0 7 4, 0 0 0 46. 5 1 5 0 × 7 8 × 8 0 4 0 0 0 48. 6 3 6 0 × 5 4 × 5 0 3 0 0 0 50. 3 5 5 4 0 0 × 2 9 9 × 3 0 0 1 2 0, 0 0 0 52. 7 8 9 8 0 0 × 4 3 4 × 4 0 0 3 2 0, 0 0 0 54. 454 ÷ 87 ≈ 450 ÷ 90 = 5 56. 1263 ÷ 29 ≈ 1260 ÷ 30 = 42 58. 3641 ÷ 571 ≈ 3600 ÷ 600 = 6 60. 32 , 854 ÷ 748 ≈ 32 , 900 ÷ 700 = 47 62. $ 4 9 8 $ 5 0 0 2 8 9 3 0 0 + 1 4 5 + 1 0 0 $ 9 0 0 64. $ 4 9 8 $ 5 0 0 2 8 9 3 0 0 6 2 1 0 0 1 5 9 2 0 0 + 3 2 0 + 3 0 0 $ 1 4 0 0 The budget covers the choices. 66. Answers will vary depending on the options chosen.

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    10 Chapter 1: Whole Numbers 68. a) Totalcost of attending: $250 · 490 = $122 , 500 Totalcost of hotelrooms: $170 · 2 · 320 = $108 , 800 Totalamount spent: $122 , 500 + $108 , 800 = $231 , 300 b) Totalcost of attending: $200 · 500 = $100 , 000 Totalcost of hotelrooms: $200 · 2 · 300 = $120 , 000 Totalamount spent: $100 , 000 + $120 , 000 = $220 , 000 70. $2211 ÷ $11 ≈ $2200 ÷ $10 = 220 rolls 72. 32 > 0 74. 28 > 18 76. 77 < 117 78. 999 > 997 80. 345 < 456 82. 12 < 32 84. 1 , 014 , 023 > 758 , 708, or 758 , 708 < 1 , 014 , 023 86. 843 , 393 > 842 , 583, or 842 , 583 < 843 , 393 88. 9 0 0 2 + 4 5 8 7 1 3 , 5 8 9 90. 8 9 9 12 9 0 0 2 / ✥✥✥ − 4 5 8 7 4 4 1 5 92. 3 4 3 0 6 × 5 8 2 4 4 8 1 5 3 0 0 1 7 , 7 4 8 94. 2 0 8 2 3 4 7 8 4 4 6 1 8 4 1 8 4 0 The answer is 208. 96. 27,060; this is close to the estimated sum found in Exercise 42. 98. 73,780; this is close to the estimated difference found in Exercise 44. Exercise Set 1.7 RC2. (a) RC4. (b) CC2. 672 = 6 · n 672 ? 6 · 112 ∣ ∣ ∣ 672 TRUE 112 is a solution. CC4. 5462 = 3189 + t 5462 ? 3189 + 2327 ∣ ∣ ∣ 5516 FALSE 2327 is not a solution. 2. 25 4. 8 6. t = 5678 + 9034 = 14 , 712 8. m = 9007 − 5667 = 3340 10. z = 34 · 15 = 510 12. w = 256 ÷ 16 = 16 14. t = 22 − 15 = 7 16. t = 16 − 16 = 0 18. x = 57 − 20 = 37 20. w = 53 − 17 = 36 22. x = 42 6 = 7 24. m = 162 9 = 18 26. y = 96 4 = 24 28. t = 741 3 = 247 30. y = 9281 − 8322 = 959 32. p = 92 − 56 = 36 34. y = 23 × 78 = 1794 36. z = 133 − 67 = 66 38. w = 3404 4 = 851 40. x = 807 − 438 = 369 42. q = 10 , 534 ÷ 458 = 23 44. x = 6080 19 = 320 46. x = 1500 20 = 75

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    Exercise Set 1.8 11 48. t = 9281 − 8322 = 959 50. n = 3004 − 1745 = 1259 52. n = 660 12 = 55 54. x = 22 , 135 233 = 95 56. z = 512 − 63 = 449 58. 1 4 2 9 1 2 7 8 9 3 7 3 6 1 8 1 8 0 The answer is 142. 60. 3 3 4 1 7 5 6 8 9 5 1 5 8 5 1 7 9 6 8 1 1 The answer is 334 R 11. 62. 342 > 339 64. 0 < 11 66. 6,375,600 68. x = 14 , 332 , 388 48 , 916 = 293 Exercise Set 1.8 RC2. Translate. RC4. Check. CC2. Let x = the number of miles by which Wednesday’s drive exceeded Thursday’s drive. Then we have 500 = x + 125. The correct answer is (b). CC4. Let x = the totalamount spent on groceries in May and June. Then we have 500 + 125 = x . The correct answer is (a). 2. Let w = the number of pounds by which the waste gener- ated annually per capita in the United States exceeds the waste generated in Denmark. Solve: 1473 + w = 1606 w = 123 lb 4. Let w = the number of pounds of waste generated annually per capita in Iceland. Solve: w + 531 = 1713 w = 1182 lb 6. Let n = the number of entries in each row. Solve: 504 ÷ 36 = n n = 14 entries 8. Let r = the number of active rotary oilrigs in 2007. Solve: r + 687 = 984 r = 297 rigs 10. Let n = the number of miles by which the length of the Nile exceeds the length of the Missouri-Mississippi. Solve: 3860 + n = 4135 n = 275 mi 12. Let p = the totalnumber of squares in the puzzl e. Solve: 15 · 15 = p p = 225 squares 14. Let c = the number of milligrams of caffeine in a 20-oz bottle of Coca Cola. Solve: 25 + 32 = c c = 57 milligrams 16. Let m = the number of minutes in a day. Solve: 60 · 24 = m m = 1440 minutes 18. Let r = the amount by which the average monthly rent in Atlanta exceeds the average monthly rent in Indianapolis. Solve: 905 + r = 1401 r = $496 per month 20. Let r = the amount of rent each sister pays. Solve: 2 r = 936 r = $468 per month 22. Let r = the amount of rent a tenant would pay for a one- bedroom apartment, on average, in Seattle during a 6- month period. Solve: 6 · 2063 = r r = $12 , 378 24. Let s = the speed limit for trucks. Solve: s + 10 = 75 s = 65 mph 26. Let q = the number of quires in a ream. Solve: 25 · q = 500 q = 20 quires

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    12 Chapter 1: Whole Numbers 28. Let s = the amount by which spending by visitors to the United States exceeded spending by Americans traveling abroad. Solve: 110 , 500 , 000 , 000 + s = 153 , 700 , 000 , 000 s = $43 , 200 , 000 , 000 30. Let c = the totalcost of the purchase. Solve: 96 · 88 = c c = $8448 32. Let w = the number of full weeks that will pass before the station must begin re-airing episodes. Solve: 5 · w = 208 w = 41 R 3, so 41 full weeks will pass and 3 episodes will be shown the following week before previously aired episodes are rerun. 34. Let l = the number of labels on each sheet. Solve: 25 · l = 750 l = 30 labels 36. Let g = the number of gallons required for 3795 mi of city driving. Solve: 3795 ÷ 23 = g g = 165 gal 38. a) Let A = the area of the court, in square feet. Solve: A = 94 · 50 A = 4700 square feet b) Let P = the perimeter of the court, in feet. Solve: P = 94 + 50 + 94 + 50 P = 288 ft c) Let a = the amount by which the area of a col- lege court exceeds the area of a high school court, in square feet. Solve: 4200 + a = 4700 a = 500 square feet 40. Let c = the number of cartons needed. Solve: 528 ÷ 12 = c c = 44 cartons 42. Let m = the distance on the map, in inches, between two cities that, in reality, are 2016 mi apart. Solve: 2016 ÷ 288 = m m = 7 in. Let r = the distance in miles, in reality, between two cities that are 8 in. apart on the map. Solve: 288 · 8 = r r = 2304 mi 44. Let m = the number of months required to pay off the loan. Solve: 7824 ÷ 163 = m m = 48 months 46. Let n = the number of 100’s in 3500. Solve: 3500 ÷ 100 = n n = 35 Let t = the number of minutes you must golf, walking, in order to lose one pound. Solve: t = 35 · 20 t = 700 min; we could also express this as 11 hr, 40 min. 48. Let n = the number of new jobs that will be created for marketing managers and accountants. n = 19 , 700 + 142 , 400 = 162 , 100 Let s = the number of new jobs that will be created for sales managers. Solve: s + 143 , 100 = 162 , 100 s = 19 , 000 jobs 50. Let F = the number of seats in first class, E = the number of seats in economy class, and T = the totalnumber of seats. Solve: 3 · 4 = F , 23 · 6 = E , and T = F + E F = 12, E = 138, T = 12 + 138 = 150 seats 52. Let c = the totalcost of the 5 video games. Solve: 5 · 64 = c c = $320 Then let n = the number of $20 bills required. Solve: 320 ÷ 20 = n n = 16 $20 bills 54. Let b = the new balance. Solve: 749 − 34 − 65 + 123 = b b = $773 56. Let l = the total length of the bookshelves, in feet. Solve: 6 · 3 = l l = 18 ft Since the total length of the bookshelves is greater than 16 ft, the shelves cannot be put side by side on the 16-ft wall. 58. 15 8 5 / 9 12 9 / 6 0 2 / ✥✥ − 1 8 4 3 7 7 5 9 60. 1 4 7 3 2 4 7 0 8 3 2 1 5 0 1 2 8 2 2 8 2 2 4 4 The answer is 147 R 4. 62. A = l × w = 211 ft × 46 ft = 9706 sq ft

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    Exercise Set 1.9 13 64. x = 81 − 15 = 66 66. Consider one student taking one class a “student-class unit.” Then let s = the totalnumber of student-cl ass units and p = the number of students taught by each instructor. Solve: 1200 · 5 = s , 4 · 30 = p s = 6000, p = 120 Now let n = the number of instructors. Solve: 6000 ÷ 120 = n n = 50 instructors Exercise Set 1.9 RC2. The expression 9 2 can be read “nine squared.” RC4. To find the average of 7, 8, and 9, we add the numbers and divide the sum by 3. CC2. Division CC4. Multiplication 2. 2 5 4. 13 3 6. 9 2 8. 1 4 10. 125 12. 64 14. 100,000 16. 64 18. (12 + 6) + 18 = 18 + 18 = 36 20. (52 − 40) − 8 = 12 − 8 = 4 22. (1000 ÷ 100) ÷ 10 = 10 ÷ 10 = 1 24. 256 ÷ (64 ÷ 4) = 256 ÷ 16 = 16 26. 2 2 + 5 2 = 4 + 25 = 29 28. (32 − 27) 3 + (19 + 1) 3 = 5 3 + 20 3 = 125 + 8000 = 8125 30. 23 + 18 · 20 = 23 + 360 = 383 32. 10 · 7 − 4 = 70 − 4 = 66 34. 90 − 5 · 5 · 2 = 90 − 50 = 40 36. 8 2 − 8 · 2 = 64 − 8 · 2 = 64 − 16 = 48 38. 1000 ÷ 25 − (15 + 5) = 1000 ÷ 25 − 20 = 40 − 20 = 20 40. 3 · 8 + 5 · 8 = 24 + 40 = 64 42. 144 ÷ 4 − 2 = 36 − 2 = 34 44. 7 · (10 − 3) 2 − 2 · (3 + 1) 2 = 7 · 7 2 − 2 · 4 2 = 7 · 49 − 2 · 16 = 343 − 32 = 311 46. 6 2 − 3 4 ÷ 3 3 = 36 − 81 ÷ 27 = 36 − 3 = 33 48. 7 2 + 20 · 4 − (28 + 9 · 2) = 7 2 + 20 · 4 − (28 + 18) = 7 2 + 20 · 4 − 46 = 49 + 20 · 4 − 46 = 49 + 80 − 46 = 83 50. 8 × 9 − (12 − 8) ÷ 4 − (10 − 7) = 8 × 9 − 4 ÷ 4 − 3 = 72 − 1 − 3 = 68 52. 80 − 2 4 · 15 ÷ (7 · 5 − 45 ÷ 3) = 80 − 2 4 · 15 ÷ (35 − 15) = 80 − 2 4 · 15 ÷ 20 = 80 − 16 · 15 ÷ 20 = 80 − 240 ÷ 20 = 80 − 12 = 68 54. 2 7 ÷ 2 5 · 2 4 ÷ 2 2 = 128 ÷ 32 · 16 ÷ 4 = 4 · 16 ÷ 4 = 64 ÷ 4 = 16 56. 86 + 92 + 80 + 78 4 = 336 4 = 84 58. $1025 + $775 + $2062 + $942 + $3721 5 = $8525 5 = $1705 60. 72 ÷ 6 − { 2 × [9 − (4 × 2)] } = 72 ÷ 6 − { 2 × [9 − 8] } = 72 ÷ 6 − { 2 × 1 } = 72 ÷ 6 − 2 = 12 − 2 = 10 62. [92 × (6 − 4) ÷ 8] + [7 × (8 − 3)] = [92 × 2 ÷ 8] + [7 × 5] = [184 ÷ 8] + 35 = 23 + 35 = 58

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