Question

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
67 ≤ x ≤ 97

78 ≤ x ≤ 95
78 ≤ x ≤ 95

80 ≤ x ≤ 90
80 ≤ x ≤ 90

86 ≤ x ≤ 87
Answer
explain
Answered by GPT 3.5
67 ≤ x ≤ 97
Answered by GPT 3.5
To find the possible values for a third quiz score that would give him an average between 80 and 90, inclusive, we can calculate the sum of the three quiz scores and divide it by 3 to find the average.

Let x represent the third quiz score. The sum of the three quiz scores is 78 + 95 + x, and the average is (78 + 95 + x)/3.

We want this average to be between 80 and 90, inclusive, so we can set up the following compound inequality:

80 ≤ (78 + 95 + x)/3 ≤ 90

Multiplying both sides of the inequality by 3 gives:

240 ≤ 78 + 95 + x ≤ 270

Now we can solve for x by subtracting 78 and 95 from all parts of the inequality:

240 - 78 - 95 ≤ x ≤ 270 - 78 - 95

Simplifying gives:

67 ≤ x ≤ 97

Therefore, the possible values for the third quiz score that would give him an average between 80 and 90, inclusive, are 67 to 97.