The sum of two consecutive odd numbers is 68. Find the numbers.

Options

A. 33, 37
B. 33,35
C. 33, 34
D. 34,35

Answer

To solve the problem of finding two consecutive odd numbers whose sum is 68, we can follow these steps:

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

### Step 2: Define the second odd number
Since we are looking for consecutive odd numbers, the next consecutive odd number can be expressed as \( x + 2 \).

### Step 3: Set up the equation
According to the problem, the sum of these two consecutive odd numbers is 68. Therefore, we can write the equation:
\[ x + (x + 2) = 68 \]

### Step 4: Simplify the equation
Combine like terms in the equation:
\[ 2x + 2 = 68 \]

### Step 5: Solve for \( x \)
Subtract 2 from both sides of the equation:
\[ 2x = 68 - 2 \]
\[ 2x = 66 \]

Now, divide both sides by 2:
\[ x = \frac{66}{2} \]
\[ x = 33 \]

### Step 6: Find the second odd number
Now that we have the first odd number, we can find the second consecutive odd number:
\[ x + 2 = 33 + 2 = 35 \]

### Step 7: State the final answer
The two consecutive odd numbers are 33 and 35.