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100 Chapter 2 Linear Equations and Inequalities in One Variable 72. The difference of twice a number and -4 is equal to 14 less that the number. 73. Four more than twice a number equals three times the number decreased by 5. 74. The ratio of a number to 4 gives the same result as onehalf of the number plus 3. 75. If five times a number is subtracted from four, the result is the same as six less than twice the number. 76. If three times a number is added to ten, the result is the same as six more than five times the number. 77. One angle is 25° more than another angle. Their sum is 180°. Find the measure of each angle. 78. One angle is 40° less than another angle. Their sum is 90°. Find the measure of each angle. 79. One angle is 19° less than another angle. Their sum is 90°. Find the measure of each angle. 80. One angle is 37° more than another angle. Their sum is 180°. Find the measure of each angle. 81. From June 2008 to June 2009, Alice Walton and Lawrence Ellison were two of the 31 richest Americans. Their combined net worth was $46.3 billion. Alice Walton earned $7.7 billion less than Lawrence Ellison. How much did each of them earn (in billions of dollars)? (Source: http://www.forbes.com/lists/) 82. From June 2008 to June 2009, Christy Walton and Forrest Edward Mars were two of the 31 richest Americans. Their combined net worth was $32.5 billion. Christy Walton earned $10.5 billion more than Forrest Edward Mars. How much did each of them earn (in billions of dollars)? (Source: http://www.forbes.com/lists/) 83. The combined total sales of a corporation in 2009 and 2010 was $69.1 billion. The total sales in 2009 was $1.5 billion less than the total sales in 2010. Let x = total sales in 2009 (in billions of dollars) and let y = total sales in 2010 (in billions of dollars). a. Write an equation using x and y that represents the combined total sales in 2009 and 2010. b. Write an equation that relates the total sales in 2010 to the total sales in 2009. 84. The total number of individual songs purchased digitally in 2008 and 2009 was 2.231 billion. The total number of individual songs purchased digitally in 2008 was 0.089 billion less than the total number in 2009. Let x = total number of individual songs purchased digitally in 2008 (in billions) and let y = total number in 2009 (in billions). (Source: http://www. ritholtz.com) a. Write an equation using x and y that represents the combined total number of individual songs purchased digitally in 2008 and 2009. b. Write an equation that relates the total number of songs purchased digitally in 2008 to the total number of songs purchased digitally in 2009. You Be the Teacher! Anita and Maria are studying together. They are solving problems requiring them to translate phrases into mathematical statements. However, the wording of the problem is ambiguous so that both of their answers are correct. Change the wording of each statement so that only Anita’s answer is correct. 85. The square of a number subtracted by 3 is 10. Anita: x2 - 3 = 10 Maria: (x - 3)2 = 10 86. The absolute value of a number added to 7 is 14. Anita: uxu + 7 = 14 Maria: ux + 7u = 14 87. Half of a number plus 2 is 6. Anita: 1 2 x + 2 = 6 Maria: 1 2 (x + 2) = 6 88. Twice a number subtracted from 12 is 23. Anita: 2(12 - x) = 23 Maria: 12 - 2x = 23 Calculate It! Use a graphing calculator to determine if the given numbers are solutions of the equation. Specify the equation(s) that were entered into the calculator. 89. 3x2 - x = 2x; x = -1, 0, 1 90. ux - 3u = 5; x=-2, 0, 2 91. 4x = x + 3 2 ; x = 0, 1 2 , 1 92. x + 1 2 = x2 - 1 4 ; x=-1, - 1 2 , 1 2 Think About It! 93. Write a statement that corresponds to the equation 2(x - 5) = x + 6. 94. Write a statement that corresponds to the equation 2x - 5 = 6x. 95. Write an equation that has x = 3 as its solution. 96. Write an equation that has x = -1 as its solution.


hendricks_beginning_algebra_1e_ch1_3
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