Class distribution of sweets: There are 40 students and 5 teachers. Each student receives sweets equal to 15% of the number of students, and each teacher receives sweets equal to 20% of the number of students. How many sweets were distributed in total?

Introduction / Context:
This problem is about interpreting percentage-based allocations relative to a fixed reference count (the number of students). Both students and teachers receive sweets calculated as percentages of the student count, not of recipients.

Given Data / Assumptions:

• Total students = 40; total teachers = 5.
• Each student gets 15% of 40 sweets.
• Each teacher gets 20% of 40 sweets.
• All distributions use whole-number arithmetic derived from the percentages.

Concept / Approach:
Compute per-recipient sweets first, since the percentage base is the number of students. Then multiply by the number of recipients in each group and add the results to obtain the total sweets needed.

Step-by-Step Solution:
Per student = 0.15 * 40 = 6 sweetsPer teacher = 0.20 * 40 = 8 sweetsStudents total = 40 * 6 = 240Teachers total = 5 * 8 = 40Grand total = 240 + 40 = 280 sweets

Verification / Alternative check:
Check bases: both percentages reference 40 students, not 45 total people, so the above multiplication is correct.

Why Other Options Are Wrong:
240 omits teacher sweets; 320 and 360 overshoot; 260 undercounts a subgroup.

Common Pitfalls:
Using the total people (45) as the percentage base or calculating different bases for students and teachers leads to incorrect totals.

Final Answer:
280