The average temperature of Monday–Thursday is 60°. The average of Tuesday–Friday is 63°. If the ratio of Monday to Friday temperatures is 21 : 25, what is Friday’s temperature?

Introduction:
Overlapping four-day averages allow elimination of common days to get a relation between Monday and Friday. The given ratio then provides absolute values. This is a standard overlapping-averages technique.

Given Data / Assumptions:
(Mon + Tue + Wed + Thu) / 4 = 60 ⇒ M + T + W + Th = 240. (Tue + Wed + Thu + Fri) / 4 = 63 ⇒ T + W + Th + F = 252. M : F = 21 : 25.

Concept / Approach:
Subtract the two four-day sums to get F − M. Combine with the ratio M : F to solve for M and F numerically.

Step-by-Step Solution:
(T + W + Th + F) − (M + T + W + Th) = 252 − 240 ⇒ F − M = 12. Let M = 21k and F = 25k (from the ratio). F − M = 25k − 21k = 4k = 12 ⇒ k = 3. Therefore, F = 25k = 25 * 3 = 75°.

Verification / Alternative check:
M = 21 * 3 = 63°. Check sums: M + T + W + Th and T + W + Th + F differ by 12, which matches F − M = 75 − 63 = 12.

Why Other Options Are Wrong:
70°, 73°, 78°, 69°: Do not satisfy both the difference F − M = 12 and the ratio M : F = 21 : 25.

Common Pitfalls:
Averaging 60 and 63 directly or using 21 : 25 incorrectly (e.g., reversing M and F). Use the subtraction step first, then apply the ratio.

Final Answer:
Friday’s temperature is 75°.