The sum of three consecutive odd numbers is 93. The smallest number is:

Options

A. a. 29
B. b. 31
C. c. 37
D. d. none of these

Answer

To solve the problem of finding the smallest of three consecutive odd numbers that sum to 93, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Consecutive Odd Numbers**:
Let the smallest odd number be \( x \). Then the next two consecutive odd numbers can be expressed as:
- First number: \( x \)
- Second number: \( x + 2 \)
- Third number: \( x + 4 \)

2. **Set Up the Equation**:
According to the problem, the sum of these three numbers is 93. Therefore, we can write the equation:
\[ x + (x + 2) + (x + 4) = 93 \]

3. **Combine Like Terms**:
Combine the terms on the left side of the equation:
\[ x + x + 2 + x + 4 = 93 \]
This simplifies to:
\[ 3x + 6 = 93 \]

4. **Isolate the Variable**:
To isolate \( 3x \), subtract 6 from both sides:
\[ 3x = 93 - 6 \]
\[ 3x = 87 \]

5. **Solve for \( x \)**:
Divide both sides by 3 to find \( x \):
\[ x = \frac{87}{3} \]
\[ x = 29 \]

6. **Identify the Consecutive Odd Numbers**:
Now that we have \( x \), we can find the three consecutive odd numbers:
- First number: \( x = 29 \)
- Second number: \( x + 2 = 31 \)
- Third number: \( x + 4 = 33 \)

7. **Conclusion**:
The smallest of these three consecutive odd numbers is:
\[ \text{Smallest number} = 29 \]

### Final Answer:
The smallest number is **29**.