Section 1.4 Linear Inequalities in One Variable 81 Answer 5. Jamie’s salary must be at least $2000. 2. Applications of Inequalities Solving a Linear Inequality Application Example 5 Beth received grades of 97, 82, 89, and 99 on her first four algebra tests.To earn an A in the course, she needs an average of 90 or more. What scores can she receive on the fifth test to earn an A? Solution: Let x represent the score on the fifth test. The average of the five tests is given by To earn an A, we have: 97 82 89 99 x Verbal model 5 Mathematical equation Simplify the numerator. Clear fractions. Simplify. 1Average of test scores2 90 97 82 89 99 x 367 x 5 5 5 a367 x 5 90 90 b 51902 367 x 450 x 83 To earn an A, Beth would have to score at least 83 on her fifth test. Skill Practice 5. Jamie is a salesman who works on commission, so his salary varies from month to month.To qualify for an automobile loan, his monthly salary must average at least $2100 for 6 months. His salaries for the past 5 months have been $1800, $2300, $1500, $2200, and $2800.What amount does he need to earn in the last month to qualify for the loan? Solving a Linear Inequality Application Example 6 The water level in a retention pond in northern California is 7.2 ft. During a time of drought, the water level decreases at a rate of 0.05 ft/day.The water level L (in ft) is given by L 7.2 0.05d, where d is the number of days after the drought begins (Figure 1-5).For which days after the beginning of the drought will the water level be less than 6 ft? 8 7 6 5 4 3 2 1 0 Water Level vs. Days of Drought 0 25 50 75 100 125 150 Water Level (ft) L 5 7.2 2 0.05d Number of Days Figure 1-5
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