In order to be invited to tutoring or extension activities, a student's performance must be at least 20 points higher or lower than an average score. If the average score is 105, which inequality represents p, the scores for students who are eligible for tutoring or extension activities?

Question

85 < p < 125
85 ≤ p ≤ 125
p < 85 or p > 125
p ≤ 85 or p ≥ 125

Answer 1

To find the inequality that represents the scores for students who are eligible for tutoring or extension activities, we start by identifying the range of scores that are 20 points higher or lower than the average score of 105.

Calculating the two limits:

• Lower limit: \(105 - 20 = 85\)
• Upper limit: \(105 + 20 = 125\)

Since students must have scores that are at least 20 points higher or lower than 105 to be eligible, we want to represent scores that are outside the range [85, 125]. In mathematical terms, this means scores can either be less than or equal to 85 or greater than or equal to 125.

Thus, the correct inequality that represents the scores for students eligible for tutoring or extension activities is:

p ≤ 85 or p ≥ 125.