A student scored 83 and 91 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 score on the third quiz.
To find the average of the three quiz scores:
(83 + 91 + x) / 3
To find the possible values for x that would give her an average between 85 and 90, inclusive:
85 ≤ (83 + 91 + x) / 3 ≤ 90
Multiplying by 3 to get rid of the fraction:
255 ≤ 174 + x ≤ 270
Subtracting 174 from each part of the compound inequality:
81 ≤ x ≤ 96
Therefore, the student needs to score between 81 and 96 on her third quiz to have an average between 85 and 90, inclusive.