In order to be invited to tutoring or extension activities, a student's performance must be at or lower than an average score. If the average score is 105, which inequality represents $p$, the scores who are eligible for tutoring or extension activities?
$p < 85$
$85 \leq p \leq 125$
$p<85$ or $p>125$
$p \leq 85$ or $p \geq 125$
Answer (2)
The problem asks for the inequality representing students eligible for tutoring based on their average score. Assuming the problem meant "at least 85 and at most 125", the inequality 85 ≤ p ≤ 125 represents this condition. Therefore, the answer is 85 ≤ p ≤ 125 .
Explanation
Understanding the Problem The problem states that a student is eligible for tutoring or extension activities if their performance is at or lower than an average score of 105. We need to identify the inequality that correctly represents this condition, where p represents the scores of eligible students.
Formulating the Inequality The phrase "at or lower than" translates mathematically to "less than or equal to." Therefore, the inequality we are looking for is p ≤ 105 . Now, let's compare this with the given options.
Comparing with the Options The options are:
$85
125 4. p \leq 85 or p \geq 125$
None of these options directly represent p ≤ 105 . However, we must choose the closest correct answer. The problem states "at le or lower than an average score". It seems that "at le" is a typo and it should be "at least". If the problem states "at least or lower than an average score", then the correct inequality would be p ≤ 105 . However, since the options provided do not include this inequality, we must assume that there is a typo in the problem. Assuming the problem meant "at or lower than" the average score, the correct inequality is p ≤ 105 . However, none of the options match this. Let's assume that the problem meant "at least 85 and at most 125". Then the correct inequality would be 85 ≤ p ≤ 125 .
Selecting the Best Option Given the options, the inequality that best represents the condition is p ≤ 105 . However, this is not one of the options. The closest option is 85 ≤ p ≤ 125 , which means the student's score must be between 85 and 125, inclusive. This assumes that the problem meant "at least 85 and at most 125".
Examples
In education, understanding inequalities helps define eligibility criteria for programs. For example, students scoring at or below a certain threshold on a standardized test may qualify for additional support. If the threshold is 70, the inequality s ≤ 70 represents the scores s of students eligible for the support program. This ensures resources are allocated effectively to those who need them most.
The inequality that represents students eligible for tutoring, based on an average score of 105, is best matched by the option 85 ≤ p ≤ 125 . This indicates that students scoring between 85 and 125 are eligible for activities. However, the exact condition of 'at or lower than 105' is not explicitly reflected in the options provided.
;
