A student scored 81 and 95 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.
To find the possible values for a third quiz score that would give an average between 85 and 90, we can set up a compound inequality.
Let's start by finding the average of the first two quiz scores:
(81 + 95) / 2 = 88
Next, we can set up the compound inequality using the average, 88, and the desired range of 85 to 90.
85 ≤ (81 + 95 + x) / 3 ≤ 90
To simplify this compound inequality, we can multiply each side by 3 to get rid of the fraction:
255 ≤ (81 + 95 + x) ≤ 270
Next, we can simplify further by subtracting 176 from each side:
79 ≤ x ≤ 94
Therefore, the possible values for a third quiz score that would give her an average between 85 and 90 are x such that 79 ≤ x ≤ 94.
85<((81+95+x)/3)<90.
85<((176+x)/3)<90
Multiply by 3:
255<(176+x)<270
Subtract 176:
79<X<94.
Third quiz between 79 and 94.