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?
Correct Answer: 75 kg
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:
From 4-person average: D = 320 − 252 = 68E = 68 + 3 = 71B + C = 316 − (D + E) = 316 − (68 + 71) = 177A = 252 − (B + C) = 252 − 177 = 75Verification / 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:
75 kg