Question

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.

Answer 1

To find the possible values for a third quiz score that would give her an average between 85 and 90, inclusive, we need to set up a compound inequality.

Let's represent the third quiz score as x.

The average of the 3 quiz scores can be calculated by summing up the scores and dividing by 3:

(83 + 91 + x) / 3

We want this average to be between 85 and 90, inclusive. So the compound inequality is:

85 ≤ (83 + 91 + x) / 3 ≤ 90

To solve this compound inequality, we can multiply each term by 3:

255 ≤ 83 + 91 + x ≤ 270

Next, we can simplify the expression:

255 ≤ 174 + x ≤ 270

Then, we can subtract 174 from each term:

255 - 174 ≤ x ≤ 270 - 174

81 ≤ x ≤ 96

Therefore, the possible values for a third quiz score that would give her an average between 85 and 90, inclusive, are between 81 and 96, inclusive.