110 Chapter 2 Linear Equations and Inequalities in One Variable For each problem: (1) assign a variable to the unknown, (2) write an equation that represents the situation, (3) solve the equation, and (4) answer the question using complete sentences. (See Objective 4.) 47. The sum of twice a number and 4 is equal to 19 more than the number. Find the number. 48. Five times the sum of a number and 6 is the same as six times the number. 49. The difference of twice a number and -7 is equal to 38 less than the number. 50. Five times the difference of a number and -9 is the same as six times the number. 51. Many jewelers mark up the price of engagement rings by as much as 300%! One jeweler buys a ring for $1250 but sells it for $5000. (The selling price is the cost to the jeweler plus the markup.) What is the markup that this jeweler adds to their cost of the ring? 52. Many college bookstores mark up the price of a textbook by 30%. If a math textbook costs the bookstore $80, but the bookstore sells it for $104, what is the markup amount? 53. The price of a roundtrip airline ticket from Atlanta, Georgia, to San Francisco, California, is $576.10. This price includes the cost of the ticket plus taxes and fees. What are the taxes and fees if the cost of the ticket is $497.21? 54. Many mortgage companies set up escrow accounts to pay a homeowner’s property taxes and insurance. With such a setup, a person’s mortgage payment includes the home loan payment plus the escrow payment. If Bailey’s monthly mortgage payment is $1210.80 and $199.61 of it is his escrow payment, what is Bailey’s monthly home loan payment? 55. A department store sells a stand mixer for $299.99. This price includes a $50 discount. What is the original price of the mixer? 56. A department store sells a gourmet single cup home brewing system for $105.96. This price includes a $6 sales tax. What is the price of the brewing system before taxes? 57. The 2010 Forbes 400 Richest Americans list included Facebook founder, Mark Zuckerberg, and Facebook co-founder, Dustin Moskovitz. The difference in Zuckerberg’s net worth and Moskovitz’s net worth was $5.5 billion. If Zuckerberg’s net worth was $4.1 billion more than twice Moskovitz’s net worth, what was the net worth of each person? (Source: http://www.forbes.com/lists/) 58. The 2010 Forbes 400 Richest Americans list included Apple founder, Steve Jobs, and Dell founder, Michael Dell. The difference in Dell’s net worth and Job’s net worth was $7.9 billion. If Dell’s net worth was $1.8 billion more than twice Job’s net worth, what was the net worth of each person? (Source: http://www.forbes.com/lists/) Mix ’Em Up! Solve each equations. 59. 3x + 1 = 2x + 1 60. 7x + 7 = 6x - 12 61. 3 - x = 11 - 2x 62. 10 - 9x = 14 - 10x 63. 3 4 x + 1 = 6 - 1 4 x 64. 5 8 x - 8 = 3 - 3 8 x 65. 2 7 x - 1 = 5 + 9 7 x 66. - 7 12 x + 2 = 5 12 x - 6 67. 3(x - 1) + 5 = 4(x - 2) -3 68. 10(2x + 3) -16 = 19x -15 69. 5.68x + 1.02 = 4.68x + 3.88 70. 4.19x + 3.64 = 3.19x - 1.45 71. 5.1x - 1.8 + 2.3x = 6.4x - 2.7 72. 4.1x - 2.1 + 0.4x = 3.5x - 1 73. 14 - 11x = 14 - 12x 74. 1.2 - 2.5x = 1.2 - 1.5x For each problem: (1) assign a variable to the unknown, (2) write an equation that represents the problem situation, (3) solve the equation, and (4) answer the question asked using complete sentences. 75. The difference of a number and 3 is -10. Find the number. 76. The difference of a number and 10 is -55. Find the number. 77. Four less than a number is -7. Find the number. 78. Eight less than a number is -19. Find the number. 79. Twice the sum of a number and 4 is equal to one more than the number. Find the number. 80. Three times the difference of a number and 8 equals twice the number. Find the number. 81. On average, Americans spent $6129 a year on food at home and away from home in 2010. If the average expenditures on food at home was $3624, what was the average expenditures on food away from home? (Source: http://www.bls.gov/news.release/cesan.nr0.htm) 82. In 2010, the difference in the average income before taxes and the average annual expenditures in the United States was $14,372. If the average income before taxes in 2010 was $62,481, what was the average annual expenditures in 2010? (Source: http://www.bls.gov/ news.release/cesan.nr0.htm) 83. In 2010, Forbes Celebrity 100 list included the two highest paid female athletes, Serena Williams and Maria Sharapova. The difference in Williams’s income and Sharapova’s income was -$5 million. If Williams’s income was $30 million less than twice Sharapova’s income, how much did each of them earn? (Source: http://www.forbes.com/lists/) 84. In 2010, Forbes Celebrity 100 list included the two of the highest paid teen stars, Taylor Swift and Miley Cyrus. The difference in Swift’s income and Cyrus’s income was -$3 million. If Swift’s income was $51 million less than twice Cyrus’s income, how much did each of them earn? (Source: http://www.forbes.com/lists/)
hendricks_beginning_intermediate_algebra_1e_ch1_3
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