Chapter 2 Test 187 SECTION 2.6 Write an equation that represents each situation, solve the equation, and write the answer in complete sentences. (See Objectives 1–5.) 83. A 46-in. LED–LCD HDTV is on sale for $1170. This is 35% off the original price. What is the original selling price of the TV? 84. A sweater is on sale for $18.90. If this price is 65% off the original price, what is the original price of the sweater? 85. A campus bookstore sells an intermediate algebra text for $101.25. This is a 25% markup on the cost the bookstore pays for the text. What does the bookstore pay for the text? 86. Bev’s salary after her raise is $44,285. Prior to the raise, her salary was $42,500. What percent raise did she receive? 87. The passenger volume at an international airport in Florida was 34.13 million in 2005 and 35.66 million in 2011. What is the percent increase in the passenger volume from 2005 to 2011? Round to one-tenth of a percent. 88. Kevin invests $8600 in two accounts. He invests $5350 in a mutual fund that pays 3.4% annual interest and the remaining amount in a money market fund that pays 2.6% annual interest. How much interest did he earn from the two accounts in 1 yr? 89. Stephanie has a collection of half-dollars and quarters. She has 40 more half-dollars than quarters. If the collection is worth $50, how many half-dollars and quarters does she have? 90. Joan has a collection of $20 bills and $1 bills. She has 29 more $20 bills than $1 bills. If the value of her collection is $1756, how many of each bill does she have? 91. Rachael needs to make 72 L of a 33.5% hydrochloric acid solution. How much 79% hydrochloric acid solution and how much 27% hydrochloric acid solution should she mix to get 72 L of a 33.5% hydrochloric acid solution? 92. A dairy farmer has two types of milk. How many gallons of a 2.5% milk fat solution and how many gallons of a 4.4% milk fat solution should be mixed to obtain 380 gal of a 2.9% milk fat solution? 93. Kyle and Bevin live 1026 mi apart. They leave their homes at the same time and drive toward one another until they meet. Kyle travels at 63 mph and Bevin travels at 72 mph. How long will it take before they meet? 94. Two planes leave an international airport in Tennessee at the same time. One plane travels west at 460 mph and the other plane travels east at 375 mph. How long will it take for the planes to be 4258.5 mi apart? 95. The sum of the two smaller of three consecutive even integers is the same as 300 less than nine times the largest integer. Find the integers. 96. A plane leaves Atlanta heading to Seattle at 6 a.m. traveling at 340 mph. A second plane leaves Atlanta heading to Seattle at 8 a.m. the same day traveling at 510 mph. How long will it take for the second plane to catch up to the first plane? SECTION 2.7 Solve each inequality. Graph the solution set and write the solution set in interval notation and in set-builder notation. (See Objectives 1–4.) 97. a + 5 ≥ -9 98. 4x - 18 > -6 99. 0.3a - 7.2 ≤ -2.4 100. 2 7 x + 1 ≥ 5 7 101. -1 < 3a + 2 < 23 102. -2 ≤ 4x + 10 ≤ 26 103. 17 - 2(x - 5) < -6x + 3 104. 6x + 2(x + 12) < 9x +15 105. 5 3 y + 3ay + 1 6 b ≥ 2 3 y - 1 2 106. -19 ≤ -2(x + 1) + 5 ≤ -1 107. -3.5 < 0.5y + 1.4 < 1.2 108. -1.6 < 0.3x - 2.8 < 12.2 Write an inequality that will solve each problem. Solve the inequality and answer the question in complete sentences. (See Objective 6.) 109. Baziz scored 67, 85, and 80 on three math tests. What score does he need on the fourth test to have at least an 80 average? 110. Shirl’s final grade in her math class is based on a weighted average. Homework counts as 10%, quizzes count as 20%, tests count as 50%, and the final exam counts as 20%. If she has a homework average of 72, a quiz average of 70, and a test average of 84, what score does she need to make on her final exam to have at least a 80 for her final grade? 111. The cost to rent a banquet facility for a wedding reception is $1250 plus $45 per person for the food. What is the number of attendees the couple can have at the reception if they have at most $9600 budgeted for the reception? 112. The cost to rent a car for a week is $280 plus $0.32 per mile. How many miles can be driven if you have at most $842 to rent the car for a week? Round to the nearest whole number. CHAPTER 2 TEST / LINEAR EQUATIONS AND INEQUALITIES IN ONE VARIABLE 1. An example of a linear equation in one variable is a. 3x + 5 - 7x b. 3x + 5 = 7x 2. A solution of x2 = 4x is a. x = -4 b. x = -2 c. x = 2 d. x = 4
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