Section 2.1 Equations and Their Solutions 99 51. From June 2008 to June 2009, Carl Icahn and Larry Page were the two of the 31 richest Americans. Their combined net worth was $25.8 billion. Carl Icahn earned $4.8 billion less than Larry Page. How much did each of them earn (in billions of dollars)? (Source: http:// www.forbes.com/lists/) 52. From June 2008 to June 2009, William Gates III and Jacqueline Mars were the two of the 31 richest Americans. Their combined net worth was $61 billion. William Gates III earned $39 billion more than Jacqueline Mars. How much did each of them earn (in billions of dollars)? (Source: http://www.forbes.com/lists/) 53. The perimeter of a rectangular garden is 32 ft. The width of the garden is 4 ft less than the length. Let l represent the length of the garden and let w represent the width of the garden. a. Write an equation in terms of l and w that represents the perimeter of the garden. b. Write an equation that relates the length of the garden to the width of the garden. 54. The perimeter of a regulation size basketball court is 288 ft. The length of the court is 44 ft more than the width. Let l represent the length of the court and let w represent the width of the court. a. Write an equation in terms of l and w that represents the perimeter of the court. b. Write an equation that relates the length of the court to the width of the court. 55. The Dixie Chicks reached number 1 on the Billboard 200 charts for their albums Taking the Long Way (2006) and Home (2002). The two albums sold a total of 1.31 million albums. The Taking the Long Way album sold 0.254 million albums less than the Home album. Let l represent the number of Taking the Long Way albums sold (in millions) and let h represent the number of Home albums sold (in millions). (Source: www.billboard.com) a. Write an equation in terms of l and h that represents the combined sales of the two albums. b. Write an equation that relates the number of Taking the Long Way albums sold to the number of Home albums sold. 56. In 2008 and 2009, a total of 802.2 million albums were sold in the United States. The number of albums sold in 2009 was 54.4 million less than the number of albums sold in 2008. Let x represent the number of albums sold in 2008 (in millions) and let y represent the number of albums sold in 2009 (in millions). (Source: http:// washingtonpost.com) a. Write an equation using x and y that represents the total number of albums sold in 2008 and 2009. b. Write an equation that relates the number of albums sold in 2009 to the number of albums sold in 2008. 57. There are about 3.1 million elementary and middle school teachers in the United States. Elementary and middle school teachers make up about half of all teachers in the United States. Let e represent the number of elementary teachers (in millions) and let m represent the number of middle school teachers (in millions). a. Write an equation using e and m that represents the number of elementary and middle school teachers in the United States. b. If t represents the total number of teachers in the United States, write an equation that relates the total number of teachers in the United States to the number of elementary and middle school teachers in the United States. (Source: U.S. Census) 58. Financial planners often recommend that a monthly house payment be no more than about 1 3 of your monthly income. If x represents a person’s monthly income and y represents the maximum recommended monthly house payment, write an equation that relates x and y. Mix ’Em Up! Determine whether each of the following is an expression or an equation. 59. 6z - 8 = 8z - 6 60. -2r2 + 12 - 13r - 46 61. 3x + 10 - 8y + 5 62. 5y2 - 20 = 18y - 35 63. -6r2 + 5 = 11r + 4 64. -7y + 16 + 11y + 14 Determine if the given numbers are solutions of the equation. 65. Is x = -4, x = -1, x = 0, x = 4, or x = 5 14 a solution of 8x - 8 = -6x - 3? 66. Is x = -7, x = -2, x = 0, x = 1, or x=- 11 4 a solution of -5x + 10 = -9x - 1? 67. Is x = -4, x = -2, x = 0, x = 5, or x = 1 2 a solution of x2 = x + 20? 68. Is x = –2, x = –1, x = 0, x = 2, or x = 1 3 a solution of x2 = –3x – 2? For each exercise, defi ne a variable and write an equation that can be used to solve the problem. 69. Twice the sum of a number and 11 is the same as five times the number. 70. Five times the difference of a number and 20 is the same as three times the number. 71. The sum of four times a number and –10 is equal to 20 more than the number.
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