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Solution Manual for Beginning Algebra, 9th Edition

Solution Manual for Beginning Algebra, 9th Edition is your go-to resource for solving complex textbook problems with clear solutions and explanations.

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     S OLUTIONS M ANUAL B EGINNING A LGEBRA N INTH E DITION John Tobey North Shore Community College Danvers, Massachusetts Jeffrey Slater North Shore Community College Danvers, Massachusetts Jamie Blair Orange Coast College Costa Mesa, California Jennifer Crawford Normandale Community College Bloomington, Minnesota

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    Contents Chapter 0 1 Chapter 1 18 Chapter 2 37 Chapter 3 71 Chapter 4 92 Chapter 5 114 Chapter 6 135 Chapter 7 165 Chapter 8 198 Chapter 9 232 Chapter 10 256 Practice Final Examination 287

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    1 Chapter 0 0.1 Exercises 2. 13 : 17 17 is the denominator 4. 1: 3 17 or 3 17 6. 3 3 4 8. 20 5 4 5 24 4 6 × = = 6× 10. 8 1 8 1 48 6 8 6 × = = × 12. 72 18 4 4 18 18 1 × = = × 14. 32 32 1 1 64 32 2 2 × = = × 16. 33 11 3 3 55 11 5 5 × = = × 18. 63 9 7 7 81 9 9 9 × = = × 20. = = 3 19 4 5 19 3 5 5 15 4 22. 7 54 5 7 54 7 7 7 49 5 = = 24. = = 6 41 5 6 41 6 6 6 36 5 26. 8 25 1 3 25 8 3 3 24 1 = = 28. 11 79 2 7 79 11 7 7 7 09 7 2 = = 30. 15 124 4 1 8 124 15 15 8 8 2 8 44 40 4 = = = 32. × + + = = = 2 (4 5) 2 20 2 22 4 5 5 5 5 34. × + + = = = 1 (5 12) 1 60 1 61 5 12 12 12 12 36. 5 (1 6) 5 6 5 11 1 6 6 6 6 × + + = = = 38. 2 (6 3) 2 18 2 20 6 3 3 3 3 × + + = = = 40. 1 (10 9) 1 90 1 91 10 9 9 9 9 × + + = = = 42. 78 78 6 6 = ÷ 13 6 78 6 18 18 0 78 13 6 =

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    Chapter 0: A Brief Review of Arithmetic Skills ISM: Beginning Algebra 2 44. × = ⇒ = × 5 ? 5 6 30 9 54 9 6 54 46. × = ⇒ = × 5 ? 5 5 25 9 45 9 5 45 48. × = ⇒ = × 13 ? 13 3 39 17 51 17 3 51 50. 10 ? 10 4 40 15 60 15 4 60 × = ⇒ = × 52. 7 ? 7 5 35 8 40 8 5 40 × = ⇒ = × 54. 45 ? 45 2 90 50 100 50 2 100 × = ⇒ = × 56. 20 5 4 5 424 106 4 106 × = = × 58. 1400 70 20 70 2420 121 20 121 × = = × 60. = + + 3 3 is raisins 1 3 1 5 62. + = + + 1 3 4 1 3 1 5 does not contain nuts 64. 6 6 3 2 3 6 8 14 7 2 7 × = = = + × 3 7 of the students enrolled in 1994 were male. Classroom Quiz 0.1 1. 56 7 8 7 88 11 8 11 × = = × 2. 11 (5 14) 11 70 11 81 5 14 14 14 14 × + + ⇒ = = 3. 109 1 9 12 12 = 9 12 109 108 1 0.2 Exercises 2. You must change the fractions to equivalent fractions with a common denominator. 4. 21 17 and 30 20 30 = 2 ⋅ 3 ⋅ 5 20 = 2 ⋅ 2 ⋅ 5 LCD = 2 ⋅ 2 ⋅ 3 ⋅ 5 = 60 6. 5 1 and 18 24 18 = 2 ⋅ 3 ⋅ 3 24 = 2 ⋅ 2 ⋅ 2 ⋅ 3 LCD = 2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 3 = 72 8. 5 7 and 16 48 16 = 2 ⋅ 2 ⋅ 2 ⋅ 2 48 = 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 3 LCD = 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 3 = 48 10. 11 7 and 12 20 12 = 2 ⋅ 2 ⋅ 3 20 = 2 ⋅ 2 ⋅ 5 LCD = 2 ⋅ 2 ⋅ 3 ⋅ 5 = 60 12. 7 8 and 30 45 30 = 2 ⋅ 3 ⋅ 5 45 = 3 ⋅ 3 ⋅ 5 LCD = 2 ⋅ 3 ⋅ 3 ⋅ 5 = 90 14. 1 3 9 , , and 7 14 35 7 = 7 14 = 2 ⋅ 7 35 = 5 ⋅ 7 LCD = 2 ⋅ 5 ⋅ 7 = 70 16. 3 5 11 , , and 8 12 42 8 = 2 ⋅ 2 ⋅ 2 12 = 2 ⋅ 2 ⋅ 3 42 = 2 ⋅ 3 ⋅ 7 LCD = 2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 7 = 168

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    ISM: Beginning Algebra Chapter 0: A Brief Review of Arithmetic Skills 3 18. 5 3 11 , and 8 14 16 8 = 2 ⋅ 2 ⋅ 2 14 = 2 ⋅ 7 16 = 2 ⋅ 2 ⋅ 2 ⋅ 2 LCD = 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 7 = 112 20. 3 5 3 5 8 11 11 11 11 + + = = 22. 11 2 11 2 9 3 15 15 15 15 5 − − = = = 24. 3 13 3 3 13 4 9 52 61 1 or 1 20 15 20 3 15 4 60 60 60 60 × × + = + = + = × × 26. 4 3 4 7 3 5 28 15 13 5 7 5 7 7 5 35 35 35 × × − = − = − = × × 28. 3 1 3 3 1 8 9 8 17 8 3 8 3 3 8 24 24 24 × × + = + = + = × × 30. 2 7 2 2 7 3 4 21 25 5 15 10 15 2 10 3 30 30 30 6 × × + = + = + = = × × 32. 21 23 21 2 23 42 23 19 12 24 12 2 24 24 24 24 × − = − = − = × 34. 13 1 13 1 3 13 3 10 2 15 5 15 5 3 15 15 15 3 × − = − = − = = × 36. 7 5 7 9 5 4 63 20 83 11 or 2 4 9 4 9 9 4 36 36 36 36 × × + = + = + = × × 38. 4 7 1 36 49 21 106 43 or 1 7 9 3 63 63 63 63 63 + + = + + = 40. 1 3 4 1 7 3 6 4 4 12 14 21 12 7 14 6 21 4 7 18 16 84 84 84 41 84 × × × + + = + + × × × = + + = 42. 1 2 11 1 3 2 5 11 5 3 15 5 3 3 5 15 3 10 11 15 15 15 2 15 × × + − = + − × × = + − = 44. + − = + − = = 5 3 1 5 9 8 6 1 24 8 3 24 24 24 24 4 46. + = + = + = = 1 1 25 13 75 52 127 7 3 2 5 8 6 8 6 24 24 24 24 48. + = + = + = = 2 3 20 3 80 9 89 5 6 7 3 4 3 4 12 12 12 12 50. − = − = − = = 2 3 37 15 148 75 73 13 7 3 3 5 4 5 4 20 20 20 20 52. 8 3 113 13 113 39 74 14 7 2 4 15 5 15 5 15 15 15 15 − = − = − = = 54. + = + = + = = 1 1 22 13 66 91 157 10 3 4 7 7 3 7 3 21 21 21 21 56. 1 2 37 17 20 2 12 5 6 3 3 3 3 3 3 − = − = = 58. 12 1 129 118 247 9 9 19 13 13 13 13 13 + = + = = 60. + = + = = 19 3 19 9 28 14 30 10 30 30 30 15 62. 2 2 17 37 85 111 196 1 5 7 13 3 5 3 5 15 15 15 15 + = + = + = = 64. − = − = = 15 3 15 9 6 1 24 8 24 24 24 4 66. 1 1 19 17 76 51 25 1 6 4 2 3 4 3 4 12 12 12 12 − = − = − = = 68. 3 1 363 261 45 26 8 10 8 10 1815 1044 40 40 771 40 11 19 40 − = − = − = = 70. 2 5 5 5 30 5 35 17 1 1 3 18 3 18 18 18 18 18 + = + = + = =

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    Chapter 0: A Brief Review of Arithmetic Skills ISM: Beginning Algebra 4 72. 3 2 31 32 155 128 283 3 7 6 14 4 5 4 5 20 20 20 20 + = + = + = = 74. 5 28 29 224 29 195 3 28 3 24 8 1 8 8 8 8 8 − = − = − = = 76. 1 1 2 21 21 56 10 5 18 2 4 3 2 4 3 126 63 224 12 12 12 413 12 5 34 12 + + = + + = + + = = They ran a total of 5 34 12 miles. 78. 3 1 2 71 5 8 17 1 2 4 4 3 4 4 3 213 15 32 12 12 12 196 12 4 16 12 1 16 3 + − = + − = + − = = = There are now 1 16 3 gallons. 80. 5 9 37 73 74 73 1 4 4 inch 8 16 8 16 16 16 16 − = − = − = It is smaller so it will slide in and out easily. 82. 1 1 5 1 40 1 41 9 2 2 2 16 2 16 16 16 16 16 + = + = + = = The fairway grass could be as long as 9 2 inches. 16 7 1 14 1 13 8 16 16 16 16 − = − = The putting greens could be as short as 13 inch. 16 Cumulative Review 83. 36 9 4 9 44 1 4 11 × = = × 84. 3 26 5 3 133 26 5 5 5 × + = = Classroom Quiz 0.2 1. 1 2 3 4 16 9 29 5 or 1 6 3 8 24 24 24 24 24 + + = + + = 2. 17 5 53 41 2 4 18 9 18 9 53 82 18 18 135 18 9 7 18 1 7 2 + = + = + = = = 3. 2 2 37 11 111 55 56 11 7 3 3 5 3 5 3 15 15 15 15 − = − = − = = 0.3 Exercises 2. Invert the second fraction. Multiply the result by the first fraction. 4. 5 28 5 7 4 4 1 or 1 7 15 7 5 3 3 3 ⋅ × = × = ⋅ 6. 17 13 17 13 1 26 34 2 13 17 2 4 × = × = ⋅ ⋅ 8. 3 5 15 11 7 77 × = 10. ⋅ × = × = ⋅ ⋅ 15 8 3 5 8 5 24 9 3 8 3 3 9 12. 6 9 2 3 9 1 21 18 3 7 2 9 7 ⋅ × = × = ⋅ ⋅ 14. 2 2 3 5 10 3 15 or 1 21 3 7 1 7 7 ⋅ × = × = ⋅ 16. 8 8 3 24 2 3 or 2 11 11 1 11 11 × = × = 18. ÷ = × = 13 13 13 7 7 9 7 9 13 9

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    ISM: Beginning Algebra Chapter 0: A Brief Review of Arithmetic Skills 5 20. ÷ = × = 7 7 1 7 4 8 8 4 32 22. 2 18 9 9 9 18 81 9 1 2 1 1 ÷ = × = × = 24. 8 5 8 6 2 4 6 4 12 6 12 5 2 6 5 5 ⋅ ÷ = × = × = ⋅ 26. 9 4 9 7 9 7 9 28 7 28 4 4 7 4 16 ÷ = × = × = ⋅ 28. 5 6 10 13 5 10 5 13 5 13 13 1 1 6 13 6 10 6 2 5 12 12 × = ÷ = × = = = × × 30. 3 4 11 12 3 11 3 12 3 3 4 9 4 12 4 11 4 11 11 × × = ÷ = × = = × 32. 1 3 9 27 9 8 4 1 4 3 1 2 8 2 8 2 27 3 3 ÷ = ÷ = × = = 34. ÷ = ÷ = × × = × = = 1 3 11 15 5 3 2 4 2 4 11 4 2 15 11 2 2 2 15 22 15 7 1 15 36. 1 7 1 15 1 8 1 2 4 2 1 4 8 4 8 4 15 4 15 15 ⋅ ÷ = ÷ = × = × = 38. 1 2 18 1 18 9 18 2 9 2 2 18 4 4 2 1 2 1 9 1 9 4 ⋅ = ÷ = ÷ = × = × = 40. 5 6 1 2 5 1 5 5 5 2 5 2 1 2 6 2 6 2 6 5 3 2 5 3 2 = ÷ = ÷ = × = × = ⋅ 42. ⋅ ⋅ × = × = ⋅ 12 9 6 2 3 3 3 18 2 6 3 2 44. 5 11 5 18 5 3 6 15 4 or 1 6 18 6 11 6 11 11 11 ⋅ ÷ = × = × = 46. ÷ = ÷ = × = × = = 2 1 92 7 10 2 9 3 9 3 92 3 9 7 92 1 3 7 92 21 8 4 21 48. 2 15 5 15 3 5 3 3 15 1 9 3 1 3 1 5 1 5 ⋅ ÷ = ÷ = × = × = 50. 1 13 2 6 6 12 78 2 2 1 ⋅ × = × = 52. 1 2 3 7 2 3 7 2 14 2 3 3 5 3 3 5 3 5 15 ⋅ × × = × × = = ⋅ 54. a. 1 24 1 4 6 4 6 15 6 15 15 ⋅ × = × = b. 1 24 1 15 1 3 5 5 6 15 6 24 2 3 24 48 ⋅ ÷ = × = × = ⋅ 56. a. 3 21 3 25 3 25 25 7 25 7 21 7 3 7 49 ÷ = × = × = ⋅ b. 3 21 3 3 7 9 7 25 7 25 25 ⋅ × = × = 58. 1 5 117 13 29 1 4 8 4 8 117 8 4 13 9 13 2 4 4 13 18 ÷ = ÷ = × ⋅ ⋅ = × = The material can make 18 pullovers. 60. 1 15 51 3 5 51 15 153 5 1 5 1 5 ⋅ ×10 = × = × = The area of her garden is 153 square feet. Cumulative Review 61. 11 11 5 55 15 75 15 5 75 ? × = ⇒ = ×

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    Chapter 0: A Brief Review of Arithmetic Skills ISM: Beginning Algebra 6 62. 7 7 7 49 9 63 9 7 63 ? × = ⇒ = × Classroom Quiz 0.3 1. 4 26 4 13 2 8 13 29 13 29 29 ⋅ × = × = 2. 1 5 11 17 187 7 5 2 15 2 6 2 6 12 12 × = × = = 3. 3 1 10 29 10 14 10 7 2 20 1 2 7 14 7 14 7 29 7 29 29 ⋅ ÷ = ÷ = × = × = 0.4 Exercises 2. We write 0.42 in words as forty-two hundredths. 4. When dividing 96.3 by 10,000 we move the decimal point 4 places to the left. 6. 0.72 18 25 18.00 0.72 25 17 5 50 50 0 = = 8. 0.6 9 15 9.0 0.6 15 9 0 0 = = 10. 0.166 1 6 1.000 0.16 6 6 40 36 40 36 4 = = 12. 5 1 0.5 10 2 = = 14. 35 7 0.35 100 20 = = 16. 775 31 25 31 0 775 1000 40 25 40 . × = = = × 18. = = 8 2 0.08 100 25 20. 48 24 2 24 4 4.8 or 4 10 5 2 5 5 × = = = × 22. × = = = × 625 25 25 25 1 6.25 or 6 1000 4 25 4 4 24. 4 64 0 23 4 87 . . . + 26. + 6.31 4.20 8.50 19.01 28. + 33.010 0.380 175.401 208.791 30. 121 52 79 85 41 67 . . . − 32. 5 0032 3 0036 1 9996 . . . − 34. 212 54 3 60 208 94 . . . − 36. 6 12 3 4 2 448 18 36 20 808 . . . × 38. 6 32 1 31 632 1 896 6 32 8 2792 . . . ×

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    ISM: Beginning Algebra Chapter 0: A Brief Review of Arithmetic Skills 7 40. × 3.84 0.0017 2688 384 0.006528 42. × 23, 000 0.0042 4 6000 92 000 96.6000 or 96.6 44. 0.3248 39 12.6672 11 7 96 78 187 156 312 312 0 46. 3.18 2.05 6.51 90 6 15 36 9 20 5 16 40 16 40 0 ∧ ∧ 48. 6.2 0.005 0.031 0 30 1 0 1 0 0 ∧ ∧ 50. 0.095 0.09 0.00 855 81 45 45 0 ∧ ∧ 52. 1.36 × 1000 = 1360 54. 175,318 ÷ 1000 = 175.318 56. 0.00243 × 100,000 = 243 58. 3.52 ÷ 1000 = 0.00352 60. 85.54 × 10,000 = 855,400 62. 96.12 ÷ 10,000 = 0.009612 64. × 8.252 0.005 0.041260 or 0.04126 66. + 1.109 0.088 16.4 17.597 68. 25712. or 25,712 0.003 77.136 6 17 15 2 1 2 1 3 3 6 6 0 ∧ ∧ 70. 25.62 × 10,000 = 256,200 72. 14.30 0.68 13.62 − 74. 0.58 ÷ 1000 = 0.00058 76. 13.2 44 52 8 528 580.8 × Chris can drive 580.8 miles. 78. 1.3 × 5 = 6.5 milligrams No; there was 0.3 milligram of copper in the 5 liters (or 0.06 milligram per liter) in excess of the standard.

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    Chapter 0: A Brief Review of Arithmetic Skills ISM: Beginning Algebra 8 Cumulative Review 79. ⋅ ÷ = ÷ = ⋅ = = ⋅ 1 1 7 21 7 4 1 2 2 3 5 2 4 2 4 2 21 1 3 3 80. ⋅ ⋅ = ⋅ = ⋅ ⋅ ⋅ 3 12 3 3 4 1 8 27 2 4 3 3 3 6 81. 12 9 48 45 48 45 93 25 20 100 100 100 100 + + = + = = 82. 3 1 8 1 16 5 16 5 11 1 1 1 5 2 5 2 10 10 10 10 10 − − = − = − = = = Classroom Quiz 0.4 1. 9.0038 4.6329 4.3709 − 2. 47.9 0.07 3.353 × 3. 25.9 0.23 5.95 7 4 6 1 35 1 15 20 7 20 7 0 ∧ ∧ Use Math to Save Money 1. $100, $300, $2000, $8000, $8000, $8000, $12,000 2. 3 × $25 + $50 + $200 + 2 × $20 = $75 + $50 + $200 + $40 = $365 3. The three smallest debts are $100 loan, $300 loan, and $2000 car loan. 4. $20 each, or $40 5. $2000 − $400 = $1600 $1600 7 $240 ≈ (rounded to the nearest whole number) It will take them 7 more months to pay off the third smallest debt. 6. Answers will vary. How Am I Doing? Sections 0.1 − 0.4 (Available online through MyMathLab or from the Instructor’s Resource Center.) 1. ⋅ = = ⋅ 15 3 5 3 55 11 5 11 2. ⋅ = = ⋅ 46 2 23 2 115 5 23 5 3. 3 15 3 4 15 3 4 4 12 3 = = 4. ⋅ + + = = = 5 4 7 5 28 5 33 4 7 7 7 7 5. × = ⇒ = × 4 ? 4 6 24 5 30 5 6 30 6. × = ⇒ = × 5 ? 5 9 45 9 81 9 9 81 7. 8 = 2 ⋅ 2 ⋅ 2 6 = 2 ⋅ 3 15 = 3 ⋅ 5 LCD = 2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 5 = 120 8. 3 2 3 2 5 7 7 7 7 + + = = 9. 5 2 5 3 2 2 15 4 19 14 21 14 3 21 2 42 42 42 ⋅ ⋅ + = + = + = ⋅ ⋅ 10. + = + ⋅ ⋅ = + ⋅ ⋅ = + = = 3 2 11 17 2 5 4 3 4 3 11 3 17 4 4 3 3 4 33 68 12 12 101 12 5 8 12 11. ⋅ − = − = − = ⋅ 17 5 17 5 2 17 10 7 18 9 18 9 2 18 18 18

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    ISM: Beginning Algebra Chapter 0: A Brief Review of Arithmetic Skills 9 12. ⋅ ⋅ − = − = − = ⋅ ⋅ 6 2 6 3 2 7 18 14 4 7 3 7 3 3 7 21 21 21 13. − = − ⋅ ⋅ = − ⋅ ⋅ = − = = 1 3 16 11 3 1 5 8 5 8 16 8 11 5 5 8 8 5 128 55 40 40 73 40 33 1 40 14. ⋅ ⋅ × = × = = ⋅ 25 14 5 5 2 7 10 1 1 7 45 7 5 9 9 9 15. ⋅ × = × = × = 1 12 7 6 2 7 12 3 42 2 1 2 1 2 16. 8 4 7 4 7 7 1 4 3 7 1 8 1 2 4 2 2 ÷ = ⋅ = × = = ⋅ 17. ÷ = ÷ = × = 1 1 7 13 7 4 28 2 3 3 4 3 4 3 13 39 18. = = 0.375 3 8 3.000 0.375 8 2 4 60 56 40 40 0 19. = = 0.833 5 6 5.000 0.83 6 4 8 20 18 20 18 2 20. 0.015 3 200 3.000 0.015 200 2 00 1 000 1 000 0 = = 21. + 15.230 3.600 0.821 19.651 22. × 3.28 0.63 984 1 968 2.0664 23. 0.45 3.015 6.7 3.0 15 0.45 6.7 2 6 8 3 35 3 35 0 = ∧ ∧ = 24. − 12.130 9.884 2.246 0.5 Exercises 2. The number directly following the word “of” should be the denominator. In this case you should use 30 80 since 80 follows the word “of.” 4. 0.54 = 54% 6. 0.063 = 6.3% 8. 0.046 = 4.6% 10. 7.49 = 749% 12. 5.7 = 570% 14. 8.674 = 867.4% 16. 6% = 0.06 18. 0.62% = 0.0062

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    Chapter 0: A Brief Review of Arithmetic Skills ISM: Beginning Algebra 10 20. 175% = 1.75 22. 8.7% = 0.087 24. 0.1% = 0.001 26. 200% = 2.00 or 2 28. 7% of 69 0.07 × 69 = 4.83 30. 25% of 600 0.25 × 600 = 150 32. 154% of 270 1.54 × 270 = 415.8 34. 49 is what percent of 28? = = 49 1.75 175% 28 36. What percent of 35 is 28? = = = 28 4 0.8 80% 35 5 38. 48 is what percent of 600? 48 2 0.08 8% 600 25 = = = 40. 75 is what percent of 30? 75 5 2 5 250 30 2 . % = = = 42. What percent of 440 is 11? 11 0 025 2 5 440 . . % = = 2.5% of the units were defective. 44. 28% of 350 0.28 × 350 = 98 98 of the new businesses failed. 46. 137 0.7611 76.11% 180 ≈ = About 76.11% had a grandparent not born in the United States. 48. 17% × 3690 = 0.17 × 3690 = 627.30 Her monthly cost is $627.30. 50. a. 65% × 18,600 = 12,090 He traveled 12,090 miles. b. 0.31 × 12,090 = 3747.90 He was paid $3747.90. 52. 729 × 688 ≈ 700 × 700 = 490,000 54. 8192 × 5984 ≈ 8000 × 6000 = 48,000,000 56. + + + ≈ + + + = 318 494 613 243 300 500 600 200 1600 58. 300, 000 16 5,846, 213 20 6, 000, 000 ≈ 60. 53, 610 50, 000 500 62.5 786 800 8 ≈ = = 62. 4.9% of $9321.88 ≈ 0.05 × $9000 = $450 64. 85 × 19 × 5 ≈ 90 × 20 × 5 = 9000 An estimated $9000 is withdrawn each hour. 66. 11, 900 10, 000 25 430 400 ≈ = It will take an estimated 25 trips. Cumulative Review 67. Distance: 69,229.5 − 68,459.5 = 770 770 22 35 = His car achieved 22 miles per gallon. 68. Total = 4.6 + 4.5 + 2.9 = 12 12 Average 4.0 inches per month. 3 = = Classroom Quiz 0.5 1. 6.4% of 380 = 0.064 × 380 = 24.32 2. 247 is what percent of 380? = = 247 0.65 65% 380 3. × ≈ × ≈ 4498.56 6721.18 4000 7000 28, 000, 000 0.6 Exercises 2. 1 1 45 25 1125 Area 22 12 2 2 2 2 4 = × = × = 1125 Cost 8.00 2250 4 = × = The total cost is $2250.

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    ISM: Beginning Algebra Chapter 0: A Brief Review of Arithmetic Skills 11 4. a. 1 1 25 41 5 12 20 5 2 2 2 2 1 5125 4 1281 25 1281 . × × = × × = = ≈ It will take 1281 cubic feet to fill the pool. b. 7.5 gal 1281 cu ft 9607.5 gal cu ft 10, 000 gal × = ≈ The pool holds 10,000 gallons. c. 10 000 2 5000 , ; = 2 × 4 = 8 They should add 8 ounces of chlorinator each day. 6. Increase from day 1 to day 3 + = 1 1 5 1 3 3 3 Jog: × = × = 5 1 5 3 1 1 2 miles 3 2 3 2 2 Walk: × = × = = 5 3 5 7 35 11 1 2 miles 3 4 3 4 12 12 Rest: × = × = = 5 1 5 5 25 1 2 4 minutes 3 2 3 2 6 6 Walk: 5 5 2 1 1 miles 3 3 3 × = = 8. Increase from day 1 to day 5 ⎛ ⎞ × × × = = ⎜ ⎟ ⎝ ⎠ 4 1 1 1 1 4 256 1 1 1 1 3 3 3 3 3 81 Jog: × = × = = 256 1 256 3 128 20 1 4 mi 81 2 81 2 27 27 She would jog 20 4 27 miles on day 5. 10. Answers will vary. Possible answer: Melinda’s trainer has the best plan because after 14 days she will be jogging and walking a gradual increase in distances. Over 14 days, Betty’s schedule increases more. The amount of increase each day is larger. Eventually it is unrealistic. 12. a. 100% − 12% = 88% 0.88 × 24 = 21.12 You get 21.12 oz from a dozen large eggs. 0.88 × 21 = 18.48 You get 18.48 oz from a dozen medium eggs. b. large: 1 79 0 085 21 12 . $ . /oz; . ≈ medium: 1 39 0 075 18 48 . $ . /oz . ≈ The medium eggs are the better buy. 14. a. From 13(b), the budget for food is $14,104.15. $14,104.15 × 0.20 = $2820.83 $14,104.15 − $2820.83 = $11,283.32 The new food budget is $11,283.32. b. $14,104.15 − $11,283.32 = $2820.83 $2820.83 would be available to reduce the debt. 16. + = ≈ = 12.56 36.28 48.84 0.04 4% 1150 1150 About 4% is deducted for retirement and medical. 18. 12.56 36.28 10.80 59.64 0.05 5% 1150 1150 + + = ≈ = Classroom Quiz 0.6 1. = 650 260 tiles 2.5 It will require 260 tiles to pave the courtyard. 2. 3% of 495,000 = 0.03 × 495,000 = 14,850. = ≈ = + 14,850 14,850 0.42 42% 20,150 14,850 35, 000 His commission was 42% of his total income. 3. 2(230) + 2(420) = 460 + 840 = 1300 2.5 × 1300 = $3250 The fence will cost $3250. Career Exploration Problems 1. 90% of the first $826 = 0.9($826) = $743.40 32% of earnings between $826 and $4980 = 0.32($4200 − $826) = 0.32($3374) = $1079.68 She has no earnings over $4980. Monthly benefit 743 40 1079 68 1823 08 $ . $ . $ . = + = Cora’s monthly benefit will be $1823.08.

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    Chapter 0: A Brief Review of Arithmetic Skills ISM: Beginning Algebra 12 2. monthly benefit 1823 08 0 434 monthly earnings 4200 $ . . $ = ≈ Cora’s benefit is about 43.4% of her pre- retirement earnings. 3. a. The reduction at age 66 is 6.7%. 100% − 6.7% = 93.3% or 0.933 0.933($1823.08) ≈ $1700.93 Cora’s monthly benefit will be $1700.93. $1823.08 − $1700.93 = $122.15 The total by which it would be reduced is $122.15. b. The reduction at age 65 is 13.3%. 100% − 13.3% = 86.7% or 0.867 0.867($1823.08) ≈ $1580.61 Cora’s monthly benefit will be $1580.61. $1823.08 − $1580.61 = $242.47 The total by which it would be reduced is $242.47. You Try It 1. a. 18 9 2 2 27 9 3 3 × = = × b. 45 15 3 3 60 15 4 4 × = = × c. 34 17 2 2 85 17 5 5 × = = × 2. a. 4 21 5 21 5 20 1 = 1 4 5 = b. 5 37 7 37 7 35 2 = 2 5 7 = 3. a. 2 2 5 2 10 2 12 2 5 5 5 5 × + + = = = b. 1 6 9 1 54 1 55 6 9 9 9 9 × + + = = = 4. 3 3 5 15 8 40 8 5 40 ? × = ⇒ = × 5. a. 10 = 2 × 5 12 = 2 × 2 × 3 LCD = 2 × 2 × 3 × 5 = 60 b. 25 = 5 × 5 20 = 2 × 2 × 5 LCD = 2 × 2 × 5 × 5 = 100 6. a. 1 1 1 9 1 2 9 2 11 2 9 2 9 9 2 18 18 18 × × + = + = + = × × b. 19 3 19 3 3 19 9 10 5 24 8 24 8 3 24 24 24 12 × − = − = − = = × 7. a. 2 1 8 28 24 28 52 7 2 3 5 3 9 3 9 9 9 9 9 + = + = + = = b. 5 1 23 4 23 8 15 5 1 3 1 2 6 3 6 3 6 6 6 2 2 − = − = − = = = 8. a. 5 2 5 2 10 11 3 11 3 33 × × = = × b. 7 15 7 3 5 1 10 21 2 5 3 7 2 ⋅ × = × = ⋅ ⋅ c. 3 6 3 18 3 6 or 3 5 1 5 5 5 × = × = 9. a. 3 2 3 5 15 14 5 14 2 28 ÷ = × = b. 7 7 7 5 5 12 5 12 7 12 ÷ = × = 10. a. 5 1 11 9 99 33 1 1 2 or 4 6 4 6 4 24 8 8 × = × = = b. 1 3 7 7 7 4 7 2 2 2 3 1 2 2 4 2 4 2 7 2 7 1 ⋅ ÷ = ÷ = × = × = = 11. 0 875 7 8 7 000 8 6 4 60 56 40 40 0 . . = 0 875 . =

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    ISM: Beginning Algebra Chapter 0: A Brief Review of Arithmetic Skills 13 12. a. 29 0 29 100 . = b. 175 7 0 175 1000 40 . = = 13. a. 2 338 6 195 8 533 . . . + b. 6 00 2 54 3 46 . . . − 14. a. 1 5 0 9 1 35 . . . × b. 5 12 0 67 3584 3 072 3 4304 . . . × 15. 18 5 0 5 9 2 5 5 4 2 4 0 2 5 2 5 0 . . . ^ ^ 16. a. 0.52 = 52% b. 0.008 = 0.8% c. 1.86 = 186% d. 0.077 = 7.7% e. 0.0009 = 0.09% 17. a. 28% = 0.28 b. 7.42% = 0.0742 c. 165% = 1.65 d. 0.25% = 0.0025 18. 15% of 92 0.15 × 92 = 13.8 19. a. What percent of 12 is 10? 10 5 0 833 83 3 12 6 . . % = ≈ = b. 50 is what percent of 40? 50 5 1 25 125 40 4 . % = = = 20. Area = 27 × 11.5 ≈ 25 × 12 = 300 The room is approximately 2 300 ft . 21. 15 ft = 5 yd 3 1 21 ft 7 yd 4 4 = 2 1 5 29 145 Area 5 7 yd 4 1 4 4 = × = × = 145 Cost 4 25 154 06 4 . . = × ≈ The tile will cost $154.06. Chapter 0 Review Problems 1. × = = × 36 12 3 3 48 12 4 4 2. 15 5 3 3 50 5 10 10 × = = × 3. × = = × 36 18 2 18 82 41 2 41 4. × = = × 18 6 3 3 30 6 5 5 5. × + + = = = 1 7 8 1 56 1 57 7 8 8 8 8 6. 6 34 4 5 34 6 5 5 30 4 = =

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