Greg has received scores of 75, 88 and 81 on his first three 100-point tests.

Question

Greg has received scores of 75, 88 and 81 on his first three 100-point tests. What score must he get on his fourth 100-point test to keep an average of 82 or greater? Express your solution as an inequality and use interval notation (Use your logic when giving the interval notation).

Answer 1

Hi Dayln,

To set this up, remember that we find an average test score by adding up the individual test scores, then dividing by the number of tests. Here, there will be four tests total but we are missing one of the scores, so we'll call the unknown test score, x.

Since the final average needs to be 82 or greater, our starting equation is:

(75 + 88 + 81 + x)/4 = 82

(244 + x)/4 = 82

(244 + x) = 328

x = 84

So to keep an average of 82, the final test score must be at least 84. To express this as an inequality we would say x is "greater than or equal to" 82 and as an interval, x = [82, 100] since 100 is the maximum test score.

Hope this helps!

Answer 2

8(75+81+88+x)/4 = 82

(244 + x)/4 = 82

244+x = 328

x = 328 - 244

= 84