A student scored 78 and 95 on his first two quizzes. Use a compound inequality to find the possible values for a third quiz score that would give him an average between 80 and 90, inclusive.
(1 point)
Responses
67 ≤ x ≤ 97
78 ≤ x ≤ 95
80 ≤ x ≤ 90
86 ≤ x ≤ 87
Let's call the third quiz score x. To find the average between 80 and 90, we need to find the sum of all three quiz scores and divide by 3:
(78 + 95 + x)/3
To obtain an average between 80 and 90, this expression must be between 80 and 90, inclusive. So, we can set up a compound inequality:
80 ≤ (78 + 95 + x)/3 ≤ 90
Now, let's simplify this inequality:
240 ≤ 78 + 95 + x ≤ 270
Subtract 173 from all parts:
67 ≤ x ≤ 97
Therefore, the correct answer is: 67 ≤ x ≤ 97