The sum of five number is 215. The average of the first two number is 36.5 and the average of the last two number is 42.5. What is the third number ?

Options

A. 52
B. 59
C. 57
D. none of these

Answer

To find the third number among five numbers whose sum is 215, we can follow these steps:

### Step 1: Understand the Given Information
We know:
- The sum of five numbers is 215.
- The average of the first two numbers is 36.5.
- The average of the last two numbers is 42.5.

### Step 2: Calculate the Sum of the First Two Numbers
The average of the first two numbers is given as 36.5. To find the sum of these two numbers, we can use the formula for average:
\[ \text{Sum of first two numbers} = \text{Average} \times \text{Number of terms} = 36.5 \times 2 = 73 \]

### Step 3: Calculate the Sum of the Last Two Numbers
Similarly, the average of the last two numbers is given as 42.5. We can calculate their sum as follows:
\[ \text{Sum of last two numbers} = \text{Average} \times \text{Number of terms} = 42.5 \times 2 = 85 \]

### Step 4: Calculate the Sum of the First Four Numbers
Now, we can find the sum of the first four numbers (the first two and the last two):
\[ \text{Sum of first two numbers} + \text{Sum of last two numbers} = 73 + 85 = 158 \]

### Step 5: Find the Third Number
We know the total sum of all five numbers is 215. To find the third number, we subtract the sum of the first four numbers from the total sum:
\[ \text{Third number} = \text{Total sum} - \text{Sum of first four numbers} = 215 - 158 = 57 \]

### Conclusion
Thus, the third number is **57**.

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