The sum of two consecutive odd numbers is 56. Find the numbers.

Options

A. 26, 27
B. 30, 31
C. 27, 29
D. 29, 31

Answer

To solve the problem of finding two consecutive odd numbers whose sum is 56, we can follow these steps:

### Step 1: Define the Variables
Let the first consecutive odd number be represented as \( x \). Since we are dealing with consecutive odd numbers, the next odd number can be expressed as \( x + 2 \).

### Step 2: Set Up the Equation
According to the problem, the sum of these two consecutive odd numbers is 56. Therefore, we can write the equation:
\[ x + (x + 2) = 56 \]

### Step 3: Simplify the Equation
Now, simplify the left side of the equation:
\[ x + x + 2 = 56 \]
This simplifies to:
\[ 2x + 2 = 56 \]

### Step 4: Isolate the Variable
Next, we need to isolate \( x \). First, subtract 2 from both sides:
\[ 2x = 56 - 2 \]
This simplifies to:
\[ 2x = 54 \]

### Step 5: Solve for \( x \)
Now, divide both sides by 2 to find the value of \( x \):
\[ x = \frac{54}{2} \]
This gives us:
\[ x = 27 \]

### Step 6: Find the Consecutive Odd Numbers
Now that we have \( x \), we can find the two consecutive odd numbers:
1. The first odd number is \( x = 27 \).
2. The second odd number is \( x + 2 = 27 + 2 = 29 \).

### Conclusion
The two consecutive odd numbers are **27 and 29**.

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