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hendricks_intermediate_algebra_1e_ch1_3

110 Chapter 2 Linear Equations and Inequalities in One Variable Objective 5 Examples Write a compound inequality that represents each situation and solve the inequality. Use a complete sentence to answer each question. 5a. Body mass index (BMI) is a measure of how much body fat a person has. A normal BMI is between 18.5 and 24.9. The formula to calculate BMI is BMI = 703w h2 , where w is weight (in pounds) and h is height (in inches). Sondra is 5 ft 4 in. tall. How much should she weigh to have a normal BMI? Round answers to the nearest whole numbers. Solution 5a. Sondra’s height in inches is 64. Her BMI is represented by 703w 642 = 703w 4096 . �� �� To determine the weight for Sondra to have a normal BMI, we need to find the solution of the following inequality. 18.5 ≤ 703w 4096 ≤ 24.9 4096(18.5) ≤ 4096a703w 4096 b ≤ 4096(24.9) 75,776 ≤ 703w ≤ 101,990.4 75,776 703 ≤ 703w 703 ≤ 101,990.4 703 107.8 ≤ w ≤ 145.1 Multiply each part by 4096. Simplify. Divide each part by 703. Approximate. Sondra should weigh between 108 and 145 lb to have a normal BMI. 5b. Neal needs to earn a B in his math class to keep his 3.0 GPA. His final grade is calculated using the following percentages: tests (45%), quizzes (20%), projects (10%), and final (25%). Neal has a 73 test average, 85 quiz average, and 82 project average. What grades could he earn on the final exam for his average to be between 80 and 89? (The maximum grade on the final exam is 100.) Solution 5b. The unknown is Neal’s final exam grade. So, we let f represent the final exam grade. Neal’s final average is computed as shown. Final average = 0.45(73) + 0.20(85) + 0.10(82) + 0.25f = 32.85 + 17 + 8.2 + 0.25f = 58.05 + 0.25f For Neal’s final average to be between 80 and 89, we solve the following inequality. 80 ≤ 58.05 + 0.25f ≤ 89 80 - 58.05 ≤ 58.05 + 0.25f - 58.05 ≤ 89 - 58.05 21.95 ≤ 0.25f ≤ 30.95 21.95 0.25f ≤ ≤ 0.25 0.25 30.95 0.25 87.5 ≤ f ≤ 123.8 Subtract 58.05 from each part. Simplify. Divide each part by 0.25. Simplify. To get a B in the course, Neal needs to score between 88 and 100 since 100 is the highest grade possible. This also tells us that Neal cannot earn a grade higher than a B, since a grade of 123.8 would be needed to earn an 89 average.


hendricks_intermediate_algebra_1e_ch1_3
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