The mean temperature from Monday to Wednesday is 37°C, and the mean temperature from Tuesday to Thursday is 34°C. If the temperature on Thursday is four-fifths of the temperature on Monday, what is the temperature (in degree Celsius) on Thursday?

Introduction / Context:
This is a temperature and average based word problem involving four days: Monday, Tuesday, Wednesday and Thursday. You are given the average temperature over two overlapping three-day periods and a relationship between Monday's and Thursday's temperatures. The task is to find the temperature on Thursday using equations and basic algebra.

Given Data / Assumptions:

• Let M, T, W, Th denote the temperatures on Monday, Tuesday, Wednesday and Thursday respectively (in °C).
• Mean temperature Monday to Wednesday is 37°C: (M + T + W) / 3 = 37.
• Mean temperature Tuesday to Thursday is 34°C: (T + W + Th) / 3 = 34.
• Thursday's temperature is four-fifths of Monday's temperature: Th = (4/5) * M.
• We must find the value of Th.

Concept / Approach:
We convert each average into an equation for the sum of the relevant temperatures. Then, we use subtraction to relate M and Th. Finally, we use the given ratio Th = (4/5)M to solve for M and then Th. It is a straightforward linear system of equations problem.

Step-by-Step Solution:
Step 1: From (M + T + W) / 3 = 37, we get M + T + W = 37 * 3 = 111. Step 2: From (T + W + Th) / 3 = 34, we get T + W + Th = 34 * 3 = 102. Step 3: Subtract the second equation from the first: (M + T + W) - (T + W + Th) = 111 - 102. This simplifies to M - Th = 9. Step 4: We also know Th = (4/5) * M. So M - (4/5)M = 9. Step 5: M * (1 - 4/5) = 9 → M * (1/5) = 9. Step 6: Therefore M = 9 * 5 = 45°C. Step 7: Now Th = (4/5) * M = (4/5) * 45 = 4 * 9 = 36°C.
Verification / Alternative check:
Check Monday to Wednesday: Only M matters here as we do not know T and W exactly, but our equations are consistent since M - Th = 9 is satisfied (45 - 36 = 9). Also Th is strictly less than M, matching the fraction 4/5. The equations are satisfied, so Th = 36°C is correct.
Why Other Options Are Wrong:
If Th = 38°C, then M - Th would not equal 9 and Th would not be 4/5 of M. The same inconsistency appears if we test 40°C, 39°C or 34°C for Thursday; they cannot satisfy both M - Th = 9 and Th = (4/5)M simultaneously.
Common Pitfalls:
Students sometimes confuse which equation to subtract from which and might incorrectly form Th - M = 9. Another common mistake is mixing up the ratio and writing M = (4/5) * Th instead of Th = (4/5) * M.
Final Answer:
The temperature on Thursday is 36 degree celsius.