Question

Aaron's math grade is the mean of his three exams. His grades on the first two exams were 83 and 92. What grade must he earn on his third exam to have an average of at least 90 for the class? (Hint: You can not get higher than 100%). Express your answer as one compound inequality.

Answer 1

His two test scores so far are 87 and 91, a total of 178.

To get an average of 90 or more on three tests, the sum of the three test scores must be 270 or more.270-178 = 92; he needs at least a 92 on the third test to average 90 or more and get an A.

Here is a faster and easier way to answer a question like this involving an average of numbers that are all close together: compare each number to the desired average to see where the total lies compared to the average.

In this problem, the desired average is 90. The first score was 87, which is -3 compared to the average; the second score was 91, which is +1 compared to the average. So the first two tests combined are -2 compare to the average.

That means the third score, in order to attain the desired average, must be +2 (at least) compared to the average: 90+2 = 92.

Any Questions or have any comments if I made a mistake, feel free to let me know or notify me.

Answer 2

95

Explanation:

Let's assume the grade Aaron must earn on his third exam is x. We have the compound inequality:

`(83+92+x)/(3)` ≥ 90

`(175 + x)/(3)` ≥ 90

175 + x ≥ 270

x ≥ 95

So, Aaron must earn a 95 on the third exam to get an average of 90 for the class.