The average temperature from Monday to Wednesday is 37°C, and the average temperature from Tuesday to Thursday is 34°C. If the temperature on Thursday is equal to four fifths of the temperature on Monday, then what is the exact temperature on Thursday in degrees Celsius?

Introduction / Context:
This question checks understanding of average (mean) temperature over overlapping time periods and the ability to translate that information into algebraic equations. The temperatures across four days are linked through averages and a proportional relationship between Monday and Thursday. The goal is to find the exact temperature on Thursday using basic algebra.

Given Data / Assumptions:

• Let the temperature on Monday be M°C.
• Let the temperature on Tuesday be T°C.
• Let the temperature on Wednesday be W°C.
• Let the temperature on Thursday be H°C.
• Average from Monday to Wednesday is 37°C, so (M + T + W) / 3 = 37.
• Average from Tuesday to Thursday is 34°C, so (T + W + H) / 3 = 34.
• Thursday temperature H is four fifths of Monday temperature M, that is H = (4/5)M.

Concept / Approach:
We use the definition of average and form linear equations. From the averages we obtain two equations in four variables, but the proportional relationship between Monday and Thursday provides a third useful equation. Solving these equations step by step allows us to eliminate T and W and obtain M and then H. This is a standard technique in algebra-based word problems.

Step-by-Step Solution:
From the first average: M + T + W = 3 * 37 = 111.From the second average: T + W + H = 3 * 34 = 102.Given H = (4/5)M.Subtract the second sum from the first: (M + T + W) - (T + W + H) = 111 - 102.This simplifies to M - H = 9.Now substitute H = (4/5)M into M - H = 9 to get M - (4/5)M = 9.This becomes (1/5)M = 9, so M = 9 * 5 = 45.Then H = (4/5)M = (4/5) * 45 = 36.

Verification / Alternative check:
Compute the three day sums using M = 45 and H = 36. We have M + T + W = 111, so T + W = 111 - 45 = 66. Also T + W + H = 102, so substituting H gives T + W + 36 = 102, hence T + W = 66. Both equations are consistent. Therefore the values satisfy all given conditions, confirming that the Thursday temperature is correct.

Why Other Options Are Wrong:
If Thursday were 35°C or 34°C, the equation H = (4/5)M would lead to a non integer or inconsistent value for M with the averages. Options 32°C and 33°C create contradictions when you recompute the averages for Monday to Wednesday and Tuesday to Thursday. Only 36°C satisfies both the average conditions and the four fifths relationship with Monday.

Common Pitfalls:
Students may incorrectly average the temperatures by adding the two averages directly or may forget to multiply by 3. Another frequent mistake is to misapply the relationship H = four fifths of M, writing M = (4/5)H by accident. Misalignment in subtraction of the two equations can also cause algebraic error. Writing each equation clearly before solving helps avoid these issues.

Final Answer:
The temperature on Thursday is 36°C.