A student scored 78 and 95 on his first two quizzes. Use a compound inequality to find the possible values for the third score that would give him an average between 80 and 90, inclusive
Let x be the third score.
We know that the average of the three scores should be between 80 and 90, inclusive.
The average can be calculated by summing the three scores and dividing by 3:
(78 + 95 + x) / 3
So, the inequality would be:
80 ≤ (78 + 95 + x) / 3 ≤ 90
Multiplying each term in the inequality by 3, we get:
240 ≤ 78 + 95 + x ≤ 270
Simplifying, we have:
373 ≤ x ≤ 177
Therefore, the possible values for the third score that would give him an average between 80 and 90, inclusive, are any scores between 177 and 373.