Section 2.8 Linear Inequalities 179 5t 7 2 6 t 4 y 6 3 7 y 4 91. 92. 93. 94. 95. 96. 1.2a 0.4 6 0.4a 2 0.4c 1.2 7 2c 0.4 2x 5 x 5 4x 6 6 5x 6 For Exercises 97–100, determine whether the given number is a solution to the inequality. 97. 98. 2x 5 6 4; x 2 3y 7 7 5; y 6 41p 72 1 7 2 p; p 1 3 k 6 211 k2; k 4 99. 100. Concept 6: Applications of Linear Inequalities For Exercises 101–110, write each English phrase as a mathematical inequality. (See Example 9.) 101. The length of a fish, L, was at least 10 in. 102. Tasha’s average test score, t, exceeded 90. 103. The wind speed, w, exceeded 75 mph. 104. The height of a cave, h, was no more than 2 ft. 105. The temperature of the water in Blue Spring, t, is no more than 72°F. 106. The temperature on the tennis court, t, was no less than 100°F. 107. The length of the hike, L, was no less than 8 km. 108. The depth, d, of a certain pool was at most 10 ft. 109. The snowfall, h, in Monroe County is between 2 in. and 5 in. 110. The cost, c, of carpeting a room is between $300 and $400. 111. The average summer rainfall for Miami, Florida, for June, July, and August is 7.4 in. per month. If Miami receives 5.9 in. of rain in June and 6.1 in. in July, how much rain is required in August to exceed the 3-month summer average? (See Example 10.) 112. The average winter snowfall for Burlington,Vermont, for December, January, and February is 18.7 in. per month. If Burlington receives 22 in. of snow in December and 24 in. in January, how much snow is required in February to exceed the 3-month winter average? 113. To earn a B in chemistry,Trevor’s average on his five tests must be at least 80. Suppose that Trevor has scored 85, 75, 72, and 82 on his first four chemistry tests. Determine the minimum score needed on his fifth test to get a B in the class. 114. In speech class, Carolyn needs at least a B to keep her financial aid.To earn a B , the average of her four speeches must be at least an 85. On the first three speeches she scored 87, 75, and 82. Determine the minimum score on her fourth speech to get a B . 115. An artist paints wooden birdhouses. She buys the birdhouses for $9 each. However, for large orders, the price per birdhouse is discounted by a percentage off the original price. Let x represent the number of birdhouses ordered.The corresponding discount is given in the table. a. If the artist places an order for 190 birdhouses, compute the total cost. b. Which costs more: 190 birdhouses or 200 birdhouses? Explain your answer. Size of Order Discount 0% 5% 10% x 49 50 x 99 100 x 199 x 200 20%
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