Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.5 - Inequalities, Compound Inequalities, and Problem Solving - Problem Set 4.5: 73

Answer

The average of the last two exams needs to be greater than 90 for him to have an average higher than 92 for all five exams.

Work Step by Step

Let x represent the score for the fourth exam, and y represent the score for the fifth exam. His average will be $\frac{96+90+94+x+y}{5}$. Because he must have an average higher than 92 for all five exams, we solve the following inequality. $\frac{96+90+94+x+y}{5}$ $\gt$ 92 Multiply both sides by 5. 96+90+94+x+y $\gt$ 460 280 + x + y $\gt$ 460 x + y $\gt$ 180 The sum of the last two exams must be greater than 180. To find their average, we divide the sum by 2. Their average is $\frac{x+y}{2}$. $\frac{x+y}{2}$ $\gt$ 90 So, their average needs to be greater than 90 for him to have an average higher than 92 for all five exams.
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