The mean temperature of Monday to Wednesday is 37 °C and of Tuesday to Thursday is 34 °C. If Thursday’s temperature is 4/5 of Monday’s temperature, what was Thursday’s temperature?

Introduction: This problem combines overlapping averages with a proportion condition between two specific days. By turning averages into equations for 3-day sums and using the 4/5 relation, we can solve for Monday and then obtain Thursday directly.

Given Data / Assumptions:

• (M + T + W) / 3 = 37 → M + T + W = 111
• (T + W + Th) / 3 = 34 → T + W + Th = 102
• Th = (4/5) * M

Concept / Approach: Subtract the two 3-day sums: (T + W + Th) − (M + T + W) = 102 − 111 = −9 → Th − M = −9 → Th = M − 9. Combine with Th = (4/5)M to solve for M, then compute Th.

Step-by-Step Solution:

Verification / Alternative check: With M = 45 and Th = 36, the difference Th − M = −9 matches the subtraction of the sums (−9), confirming consistency.

Why Other Options Are Wrong: 35.5°, 34°, and 36.5° fail the system of equations. 33° does not satisfy the 4/5 proportion when paired with any integer Monday consistent with the sums.

Common Pitfalls: Averaging the averages or ignoring the given proportion; always convert to linear equations first.

Final Answer: 36° C