The sum of three consecutive odd numbers is 57. Find the numbers.

Answer

To solve the problem of finding three consecutive odd numbers whose sum is 57, we can follow these steps:

### Step 1: Define the Variables
Let the first odd number be represented as \( x \). Since we are looking for three consecutive odd numbers, the next two numbers can be expressed as:
- First odd number: \( x \)
- Second odd 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 57. Therefore, we can set up the equation:
\[ x + (x + 2) + (x + 4) = 57 \]

### Step 3: Simplify the Equation
Now, let's simplify the left side of the equation:
\[ x + x + 2 + x + 4 = 57 \]
Combining like terms, we have:
\[ 3x + 6 = 57 \]

### Step 4: Solve for \( x \)
Next, we need to isolate \( x \). We can do this by first subtracting 6 from both sides of the equation:
\[ 3x + 6 - 6 = 57 - 6 \]
This simplifies to:
\[ 3x = 51 \]
Now, divide both sides by 3:
\[ x = \frac{51}{3} \]
Calculating this gives:
\[ x = 17 \]

### Step 5: Find the Three Odd Numbers
Now that we have \( x \), we can find the three consecutive odd numbers:
- First number: \( x = 17 \)
- Second number: \( x + 2 = 17 + 2 = 19 \)
- Third number: \( x + 4 = 17 + 4 = 21 \)

### Conclusion
The three consecutive odd numbers are:
\[ 17, 19, \text{ and } 21 \]

---