The average temperature of the first 4 days of a week was 37°C and that of the last 4 days of the week was 41°C. If the average temperature of the whole week was 39°C, the temperature of the fourth day was:

Options

A. `38^(@) C`
B. `38.5^(@) C`
C. `39^(@)C`
D. `40^(@)` C

Answer

To find the temperature of the fourth day, we can follow these steps:

### Step 1: Calculate the sum of the temperatures for the first 4 days
Given that the average temperature of the first 4 days is 37°C, we can use the formula for average:

\[ \text{Average} = \frac{\text{Sum of temperatures}}{\text{Number of days}} \]

Thus, the sum of the temperatures for the first 4 days is:

\[ \text{Sum of first 4 days} = \text{Average} \times \text{Number of days} = 37 \times 4 = 148 \text{°C} \]

### Step 2: Calculate the sum of the temperatures for the last 4 days
Similarly, for the last 4 days, the average temperature is given as 41°C. Therefore, the sum of the temperatures for the last 4 days is:

\[ \text{Sum of last 4 days} = 41 \times 4 = 164 \text{°C} \]

### Step 3: Calculate the total sum of the temperatures for the whole week
The average temperature for the whole week (7 days) is given as 39°C. Thus, the total sum of the temperatures for the week is:

\[ \text{Total sum for 7 days} = 39 \times 7 = 273 \text{°C} \]

### Step 4: Set up the equation to find the temperature of the fourth day
Let \( T_4 \) be the temperature of the fourth day. The sum of the first 4 days includes the fourth day, while the sum of the last 4 days also includes the fourth day. Therefore, we can express the total sum of the temperatures as:

\[ \text{Sum of first 4 days} + \text{Sum of last 4 days} - T_4 = \text{Total sum for 7 days} \]

Substituting the values we calculated:

\[ 148 + 164 - T_4 = 273 \]

### Step 5: Solve for \( T_4 \)
Now, we can simplify and solve for \( T_4 \):

\[ 312 - T_4 = 273 \]

Rearranging gives:

\[ T_4 = 312 - 273 = 39 \text{°C} \]

### Conclusion
The temperature of the fourth day is **39°C**.

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