a student scored 93 and 91 on her first two quizzes. write and solve a comound inequality to find the possible values for a third quiz score that would give her an average between 85 and 90, inclusive.

Answer 1

Let's call the third quiz score "x".
To find the average, we need to sum up the three quiz scores and divide by 3.
So, the average is (93 + 91 + x)/3.

We want the average to be between 85 and 90, inclusive. This means the average should be greater than or equal to 85 and less than or equal to 90.

So, we can write the compound inequality as:
85 ≤ (93 + 91 + x)/3 ≤ 90.

To solve this compound inequality, we can start by multiplying all parts of the inequality by 3 (to eliminate the denominator):
3 * 85 ≤ 3 * [(93 + 91 + x)/3] ≤ 3 * 90.
255 ≤ 93 + 91 + x ≤ 270.

Next, we can simplify the inequality:
255 ≤ (93 + 91 + x) ≤ 270.

To isolate the "x" term, we can subtract 93 and 91 from all parts of the inequality:
255 - 93 ≤ (93 + 91 + x) - (93 + 91) ≤ 270 - 93.

162 ≤ x ≤ 177.

Therefore, the possible values for the third quiz score that would give her an average between 85 and 90, inclusive, are any values between 162 and 177 (both inclusive).