The sum of three consecutive odd natural numbers is 147. Then, the middle number is:

Options

A. 47
B. 48
C. 49
D. 51

Answer

To find the middle number of three consecutive odd natural numbers that sum up to 147, we can follow these steps:

### Step 1: Define the consecutive odd numbers
Let the three consecutive odd natural numbers be:
- First odd number: \( x \)
- Second odd number (middle number): \( x + 2 \)
- Third odd number: \( x + 4 \)

### Step 2: Set up the equation
According to the problem, the sum of these three numbers is 147. Therefore, we can write the equation as:
\[ x + (x + 2) + (x + 4) = 147 \]

### Step 3: Simplify the equation
Combine like terms:
\[ 3x + 6 = 147 \]

### Step 4: Solve for \( x \)
Subtract 6 from both sides:
\[ 3x = 147 - 6 \]
\[ 3x = 141 \]
Now, divide both sides by 3:
\[ x = \frac{141}{3} = 47 \]

### Step 5: Find the middle number
Now that we have \( x \), we can find the middle number:
\[ \text{Middle number} = x + 2 = 47 + 2 = 49 \]

### Conclusion
The middle number of the three consecutive odd natural numbers is **49**.

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