on two tests so far this year a student received a 78 and a 93 the student want an average between 80 and 90 inclusive what are all of the possible scores for the third test so that the student falls within this average

Answer 1

Recall that the average score is the sum of the scores, divided by the number of tests. So, you need to have

80 <= (78+93+x)/3 <= 90
240 <= 171+x <= 270

Now can you determine the needed range of scores?

Answer 2

could you explain more because I understand that 78+93=171 and then you divide it by 2 which is 85.5

Answer 3

The students wants an average between 80 and 90 for THREE tests, not two
So far we have two and that sum is 171
So Steve said the average is
()78+93+x)/3 or (171+x)/3

we want that to be between 80 and 90, so

80 ≤ (171+x)/3 ≤ 90
everybody times 3
240 ≤ 171+x ≤ 270
subtract 171 from everybody
69 ≤ x ≤ 99

We can't make it any easier than that.