Combining overlapping triples to deduce a five-person average: The average weight of P, T, and R is 54 1/3 kg, and the average weight of T, F, and G is 53 kg. What is the average weight of P, T, R, F, and G?

Introduction / Context:
We are given two overlapping three-person averages that share T. The question asks for the five-person average of P, T, R, F, and G. We need the sum of these five, but T appears in both triples and is unknown individually.

Given Data / Assumptions:

• (P + T + R)/3 = 54 1/3 → P + T + R = 163/3
• (T + F + G)/3 = 53 → T + F + G = 159

Concept / Approach:
Sum of five S = (P + T + R) + (T + F + G) − T = 163/3 + 159 − T. Because T is unknown, S cannot be uniquely determined; many values of T satisfy the given equations with different S.

Step-by-Step Explanation:
Compute (P + T + R) = 163/3Compute (T + F + G) = 159S = 163/3 + 159 − T (depends on T)

Verification / Alternative check:
Pick two different T values that keep both equations valid (by adjusting P + R and F + G accordingly); S changes with T, proving non-uniqueness.

Why Other Options Are Wrong:
Any specific numeric average (e.g., 53.8, 52.4, 53.4, 54.0) implies a fixed S, which we cannot infer uniquely without T.

Common Pitfalls:
Assuming the shared member’s weight cancels out. It does not because it appears once positively after correcting for double counting.

Final Answer:
Cannot be determined