A student scored 84 and 87 on their first two quizzes. Write and solve a compound inequality to find the possible values for a third quiz score that would give them an average between 85 and 90, inclusive

1 answer

Let x be the score on the third quiz.

To find the average score between 85 and 90, inclusive, we can set up the compound inequality as follows:

(84 + 87 + x)/3 ≥ 85 and (84 + 87 + x)/3 ≤ 90

Solving the left side of the inequality:

(84 + 87 + x)/3 ≥ 85
(171 + x)/3 ≥ 85
171 + x ≥ 255
x ≥ 84

Solving the right side of the inequality:

(84 + 87 + x)/3 ≤ 90
(171 + x)/3 ≤ 90
171 + x ≤ 270
x ≤ 99

Therefore, the student must score between 84 and 99 on the third quiz in order to have an average between 85 and 90, inclusive.