Question

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?
a ( 85 < p < 125 )
b ( 85 leq p leq 125 )
c ( p > 85 ) or ( p > 125 )
d ( p leq 85 ) or ( p geq 125 )

Explanation:

Step1: Calculate lower threshold

$105 - 20 = 85$

Step2: Calculate upper threshold

$105 + 20 = 125$

Step3: Define eligibility condition

Eligible scores are at least 20 points lower ($p \leq 85$) or at least 20 points higher ($p \geq 125$) than the average.

Answer:

$\boldsymbol{p \leq 85 \text{ or } p \geq 125}$ (matches the fourth option)