The average temperature of Monday–Thursday is 38 °C and of Tuesday–Friday is 40 °C. If Monday was 30 °C, what was the temperature on Friday?

Introduction:
This moving-average style problem compares two consecutive 4-day averages that share three common days. Subtracting the shared sums isolates the difference between Friday and Monday, allowing direct computation of Friday’s temperature from Monday’s value and the two averages.

Given Data / Assumptions:

• Average(Mon–Thu) = 38 °C → M + T + W + Th = 152
• Average(Tue–Fri) = 40 °C → T + W + Th + F = 160
• M = 30 °C

Concept / Approach:
Subtract the first 4-day sum from the second: (T + W + Th + F) − (M + T + W + Th) = 160 − 152 = 8, giving F − M = 8. Then substitute M = 30 °C to find F.

Step-by-Step Solution:

Verification / Alternative check:
Compute T + W + Th from the first equation: T + W + Th = 152 − 30 = 122. Then from the second, F = 160 − 122 = 38 °C, confirming the result.

Why Other Options Are Wrong:
39° or 40° would imply different 4-day sums; 30° repeats Monday and contradicts the 8-degree difference; 37° does not satisfy both averages simultaneously.

Common Pitfalls:
Attempting to solve for each daily temperature separately; only the difference F − M is needed thanks to overlapping windows.

Final Answer:
38°