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
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?
could you explain more because I understand that 78+93=171 and then you divide it by 2 which is 85.5
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.
To determine the possible scores for the third test, we need to find the range of scores that would result in an average between 80 and 90 inclusive.
To find the average, we sum all the scores (sum of the two test scores obtained so far, plus the possible third score) and divide by the total number of tests (3 in this case).
Let's denote the third test score as x. We can set up an equation to represent the average:
(78 + 93 + x) / 3 = average
We know the desired average falls between 80 and 90, so we can write the following inequality:
80 ≤ (78 + 93 + x) / 3 ≤ 90
Now, let's solve the inequality step by step to find the range of possible scores for the third test:
1. Multiply each side of the inequality by 3 to eliminate the fraction:
240 ≤ 78 + 93 + x ≤ 270
2. Simplify both sides of the inequality:
240 ≤ 171 + x ≤ 270
3. Subtract 171 from all three parts of the inequality:
240 - 171 ≤ x ≤ 270 - 171
4. Simplify both sides of the inequality:
69 ≤ x ≤ 99
Therefore, the possible scores for the third test, so that the student falls within the desired average range of 80 to 90 inclusive, are any scores between 69 and 99 (inclusive).