Chain replacement and averages: A, B, C average 84 kg. Adding D yields a new average 80 kg. If E (weighing 3 kg more than D) replaces A, then the average of B, C, D, E is 79 kg. What is A’s weight?

Introduction / Context:
This problem combines two average transformations: first adding a member, then replacing a member with another whose weight is defined relative to the added member. Solving sequentially with totals yields A's weight.

Given Data / Assumptions:

• Average(A,B,C) = 84 ⇒ A + B + C = 252.
• Average(A,B,C,D) = 80 ⇒ A + B + C + D = 320 ⇒ D = 68.
• E = D + 3 = 71.
• Average(B,C,D,E) = 79 ⇒ B + C + D + E = 316.

Concept / Approach:
Use totals to isolate the unknowns: obtain D, then E, then compute B + C, and finally deduce A from A + (B + C) = 252.

Step-by-Step Solution:

Verification / Alternative check:
Check the second condition: B + C + D + E = 177 + 68 + 71 = 316 ⇒ average 316/4 = 79. Consistent.

Why Other Options Are Wrong:

• 70, 72, 80 kg: Do not satisfy all given averages simultaneously.

Common Pitfalls:
Forgetting to recompute totals after the replacement step or mixing the 3 kg offset direction for E relative to D.

Final Answer: