Your test scores in one class are 78
and 84
.
What possible scores can you earn on your next test to have a test average between 81
and 87
,
inclusive?
Question content area bottom
Part 1
Your score on the third test must be between enter your response here
and enter your response here
,
inclusive.
(Use ascending order.)
To find the possible scores on the third test, we need to determine the average of the three test scores.
To have an average between 81 and 87, we can set up the following inequality:
81 ≤ (78 + 84 + x) / 3 ≤ 87
Where x represents the score on the third test.
Now, let's solve this inequality:
81 ≤ (78 + 84 + x) / 3 ≤ 87
Multiply all sides of the inequality by 3:
243 ≤ 162 + 168 + 3x ≤ 261
Combine like terms:
243 ≤ 330 + 3x ≤ 261
Subtract 330 from all sides:
-87 ≤ 3x ≤ -69
Divide all sides by 3:
-29 ≤ x ≤ -23
So, the possible scores on the third test to have a test average between 81 and 87, inclusive, are -29, -28, -27, -26, -25, -24, and -23.