This problem describes a scenario with students enrolled in Basic Algebra and/or playing basketball, with a total of 500 students. Let's break down the given information:

• Total students: 500
• Students enrolled in Basic Algebra: 125
• Students playing basketball: 52
• Students enrolled in both Basic Algebra and basketball: 300

We can use a Venn diagram or a simple set theory approach to solve the problem.

Let's define the sets:

• Let A be the set of students enrolled in Basic Algebra.
• Let B be the set of students playing basketball.

Now let's solve each question step by step:

1. How many students are enrolled in Basic Algebra only?

   • Students enrolled in Basic Algebra but not playing basketball:
     $|A| - |A \cap B| = 125 - 52 = 73$.

2. How many students play basketball only?

   • Students playing basketball but not enrolled in Basic Algebra:
     $|B| - |A \cap B| = 300 - 52 = 248$.

3. How many students are enrolled in both Basic Algebra and basketball?

   • This is directly given as $|A \cap B| = 52$.

4. How many students are neither enrolled in Basic Algebra nor playing basketball?

   • The total number of students is 500. We subtract those involved in Basic Algebra or basketball (or both):
     $500 - (73 + 248 + 52) = 127$.

5. How many students are not enrolled in Basic Algebra?

   • Students not in Basic Algebra are the total students minus those in Basic Algebra:
     $500 - 125 = 375$.

Would you like a detailed Venn diagram or further clarification on these calculations?

Related questions:

1. How can we calculate the number of students involved in at least one activity?
2. What is the formula for determining those not involved in either activity?
3. How can we express the problem using set notation?
4. How many students are either in Basic Algebra or playing basketball but not both?
5. What percentage of students play basketball only?

Tip: Using Venn diagrams is a powerful tool for visualizing relationships between sets in such problems.