196 Chapter 2 Linear Equations and Inequalities 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. L 10 102. Tasha’s average test score, t, exceeded 90. t 7 90 103. The wind speed, w, exceeded 75 mph. w 7 75 104. The height of a cave, h, was no more than 2 ft. h 2 105. The temperature of the water in Blue Spring, t, is no more than 72°F. t 72 106. The temperature on the tennis court, t, was no less than 100°F. t 100 107. The length of the hike, L, was no less than 8 km. L 8 108. The depth, d, of a certain pool was at most 10 ft. d 10 109. The snowfall, h, in Monroe County is between 2 in. and 5 in. 2 6 h 6 5 110. The cost, c, of carpeting a room is between $300 and $400. 300 6 c 6 400 111. 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.) More than 10.2 in. of rain is needed. 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? More than 10.1 in. of snow is needed. 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. Trevor needs at least 86 to get a B in the course. 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 . Carolyn needs at least 96 on her last speech. 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. $1539 200 birdhouses cost $1440. It is cheaper to purchase 200 birdhouses because the discount is greater. 116. A wholesaler sells T-shirts to a surf shop at $8 per shirt. However, for large orders, the price per shirt is discounted by a percentage off the original price. Let x represent the number of shirts ordered. The corresponding discount is given in the table. a. If the surf shop orders 50 shirts, compute the total cost. b. Which costs more: 148 shirts or 150 shirts? Explain your answer. Size of Order Discount 0% 5% 10% x 49 50 x 99 100 x 199 x 200 20% $384 Number of Shirts Ordered Discount 0% 2% 4% 6% x 24 25 x 49 50 x 99 100 x 149 x 150 8% It costs $1112.96 for 148 shirts and $1104.00 for 150 shirts. 150 shirts cost less than 148 shirts because the discount is greater. 117. A cell phone provider offers one plan that charges $4.95 for the text messaging feature plus $0.09 for each individual incoming or outgoing text. Alternatively, the provider offers a second plan with a flat rate of $18.00 for unlimited text messaging. How many text messages would result in the unlimited option being the better deal? If there were more than 145 text messages, the unlimited option would be a better deal. Writing Translating Expression Geometry Scientific Calculator Video
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