The daily average temperatures in Chennai for the 7 days of a week were recorded. The average temperatures on Sunday, Monday and Tuesday were `20^(@) C, 38^(@)` C & `32^(@)` C respectively. The average temperatures on Thursday , Friday and Saturday were `29^(@) C, 22^(@) C and 30^(@) C` respectively . If the average of average temperatures on the first three days of the week beginning with Sunday equals that of the last four days, find the temperature on Wednesday

Answer

To solve the problem step by step, we need to find the temperature on Wednesday based on the average temperatures provided for the week.

### Step 1: Identify the average temperatures for the first three days
The average temperatures for Sunday, Monday, and Tuesday are:
- Sunday: 20°C
- Monday: 38°C
- Tuesday: 32°C

### Step 2: Calculate the total temperature for the first three days
Total temperature for Sunday, Monday, and Tuesday:
\[ 20 + 38 + 32 = 90 \text{°C} \]

### Step 3: Calculate the average temperature for the first three days
Average temperature for the first three days:
\[ \text{Average} = \frac{\text{Total temperature}}{\text{Number of days}} = \frac{90}{3} = 30 \text{°C} \]

### Step 4: Identify the average temperatures for the last three days
The average temperatures for Thursday, Friday, and Saturday are:
- Thursday: 29°C
- Friday: 22°C
- Saturday: 30°C

### Step 5: Calculate the total temperature for the last three days
Total temperature for Thursday, Friday, and Saturday:
\[ 29 + 22 + 30 = 81 \text{°C} \]

### Step 6: Set up the equation for the average temperature of the last four days
We need to include Wednesday's temperature (let's denote it as \( W \)) in the calculation for the last four days (Wednesday, Thursday, Friday, Saturday). The total temperature for these four days is:
\[ W + 29 + 22 + 30 = W + 81 \]

### Step 7: Calculate the average temperature for the last four days
The average temperature for the last four days should equal the average of the first three days, which is 30°C:
\[ \frac{W + 81}{4} = 30 \]

### Step 8: Solve for Wednesday's temperature \( W \)
Multiply both sides by 4 to eliminate the fraction:
\[ W + 81 = 120 \]
Now, isolate \( W \):
\[ W = 120 - 81 = 39 \text{°C} \]

### Conclusion
The temperature on Wednesday is **39°C**.

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