The sum of three consecutive odd number is 81. The middle number is

Options

A. `25`
B. `27`
C. `31`
D. `29`

Answer

To solve the problem of finding the middle number of three consecutive odd numbers that sum to 81, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Odd Numbers:**
Let the first odd number be represented as \( x \). Since we are dealing with consecutive odd numbers, the second odd number will be \( x + 2 \) and the third odd number will be \( x + 4 \).

2. **Set Up the Equation:**
According to the problem, the sum of these three consecutive odd numbers is 81. Therefore, we can write the equation:
\[ x + (x + 2) + (x + 4) = 81 \]

3. **Combine Like Terms:**
Simplifying the left side of the equation:
\[ x + x + 2 + x + 4 = 81 \]
This simplifies to:
\[ 3x + 6 = 81 \]

4. **Isolate the Variable:**
To isolate \( 3x \), subtract 6 from both sides:
\[ 3x = 81 - 6 \]
Simplifying this gives:
\[ 3x = 75 \]

5. **Solve for \( x \):**
Now, divide both sides by 3 to find \( x \):
\[ x = \frac{75}{3} = 25 \]

6. **Find the Middle Number:**
The middle number is the second odd number, which is \( x + 2 \):
\[ \text{Middle number} = 25 + 2 = 27 \]

### Conclusion:
The middle number of the three consecutive odd numbers is **27**.