On the past two quizzes, a student scored a 75 and 83. Write and solve a compound inequality to find the possible values for the 3rd quiz score that would give her an average between 85 and 90, inclusive.

Answer 1

Let x represent the score on the third quiz.
The average of the three quizzes is given by the expression: (75 + 83 + x)/3.
We want the average to be between 85 and 90, inclusive, so we can write the compound inequality as follows:

85 ≤ (75 + 83 + x)/3 ≤ 90.

To solve this compound inequality, we can multiply all parts by 3 to eliminate the fraction:

85*3 ≤ (75 + 83 + x) ≤ 90*3.

Simplifying, we get:

255 ≤ 158 + x ≤ 270.

Now, subtracting 158 from all parts:

255 - 158 ≤ 158 + x - 158 ≤ 270 - 158.

Simplifying further:

97 ≤ x ≤ 112.

Therefore, the possible values for the third quiz score that would give her an average between 85 and 90, inclusive, are 97, 98,..., 111, 112.