A student scored 84 and 87 on her first two quizzes. Write and solve a compound inequality to find the possible values for a third quiz score that would give her an average between 85 and 90, inclusive.
Let x be the third quiz score. The average of the three quiz scores is (84 + 87 + x)/3.
To find the possible values for x that would give her an average between 85 and 90, inclusive, we can write the following compound inequality:
85 ≤ (84 + 87 + x)/3 ≤ 90
To solve this compound inequality, we simplify it:
255 ≤ 171 + x ≤ 270
Subtracting 171 from all parts of the inequality:
84 ≤ x ≤ 99
Therefore, the possible values for the third quiz score to give her an average between 85 and 90, inclusive, are any score between 84 and 99.