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

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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