Find four consecutive odd numbers whose sum is 136.

Answer

To find four consecutive odd numbers whose sum is 136, 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 next three odd numbers
Since we are looking for consecutive odd numbers, the next three odd numbers can be expressed as:
- Second odd number: \( x + 2 \)
- Third odd number: \( x + 4 \)
- Fourth odd number: \( x + 6 \)

### Step 3: Set up the equation for their sum
According to the problem, the sum of these four consecutive odd numbers is 136. Therefore, we can write the equation:
\[ x + (x + 2) + (x + 4) + (x + 6) = 136 \]

### Step 4: Simplify the equation
Now, we will simplify the left side of the equation:
\[ x + x + 2 + x + 4 + x + 6 = 136 \]
Combining like terms, we get:
\[ 4x + 12 = 136 \]

### Step 5: Solve for \( x \)
Next, we will isolate \( x \) by first subtracting 12 from both sides:
\[ 4x = 136 - 12 \]
\[ 4x = 124 \]
Now, divide both sides by 4:
\[ x = \frac{124}{4} \]
\[ x = 31 \]

### Step 6: Find the four consecutive odd numbers
Now that we have \( x \), we can find the four consecutive odd numbers:
- First number: \( x = 31 \)
- Second number: \( x + 2 = 33 \)
- Third number: \( x + 4 = 35 \)
- Fourth number: \( x + 6 = 37 \)

### Final Answer
The four consecutive odd numbers are **31, 33, 35, and 37**.

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