Find three consecutive odd numbers whose sum is 147.

Options

A. `41,43,45`
B. `45,47,49`
C. `47,49,51`
D. `49,51,53`

Answer

To find three consecutive odd numbers whose sum is 147, we can follow these steps:

### Step 1: Define the first odd number
Let the first odd number be \( x \).

### Step 2: Define the next two consecutive odd numbers
Since we are looking for consecutive odd numbers, the next two odd numbers can be expressed as:
- Second odd number: \( x + 2 \)
- Third odd number: \( x + 4 \)

### Step 3: Set up the equation for their sum
According to the problem, the sum of these three consecutive odd numbers is 147. Therefore, we can write the equation:
\[ x + (x + 2) + (x + 4) = 147 \]

### Step 4: Simplify the equation
Combine like terms:
\[ x + x + 2 + x + 4 = 147 \]
This simplifies to:
\[ 3x + 6 = 147 \]

### Step 5: Solve for \( x \)
To isolate \( x \), subtract 6 from both sides:
\[ 3x = 147 - 6 \]
\[ 3x = 141 \]
Now, divide both sides by 3:
\[ x = \frac{141}{3} \]
\[ x = 47 \]

### Step 6: Find the three consecutive odd numbers
Now that we have \( x \), we can find the three consecutive odd numbers:
- First odd number: \( x = 47 \)
- Second odd number: \( x + 2 = 47 + 2 = 49 \)
- Third odd number: \( x + 4 = 47 + 4 = 51 \)

### Conclusion
The three consecutive odd numbers are 47, 49, and 51.

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