Three-person average weights: The average weight of A, B, and C is 45 kg. The average of A and B is 40 kg, and the average of B and C is 43 kg. Find the weight of B.

Introduction / Context:
This is a system-of-equations average problem. Translating averages to totals creates linear equations that can be combined to isolate one person’s weight.

Given Data / Assumptions:

• A + B + C average = 45 kg, so total 135 kg
• A + B average = 40 kg, so total 80 kg
• B + C average = 43 kg, so total 86 kg

Concept / Approach:
Add the two pair totals: (A + B) + (B + C) = A + 2B + C. Also note A + C = (A + B + C) - B. Substitute and solve for B.

Step-by-Step Solution:

Verification / Alternative check:
If B = 31, then A + C = 104. Pair sums: A + B = 80 gives A = 49; B + C = 86 gives C = 55. Check total: 49 + 31 + 55 = 135, average 45, consistent.

Why Other Options Are Wrong:

• 17, 20, 26, 35 kg: do not satisfy all three average conditions simultaneously.

Common Pitfalls:
Mixing up which totals to add or subtract and forgetting that average times count equals total.

Final Answer:
31 kg