The sum of two consecutive odd number is 36. the smaller one is

Options

A. `15`
B. `17`
C. `19`
D. `13`

Answer

To solve the problem of finding the smaller of two consecutive odd numbers whose sum is 36, we can follow these steps:

### Step 1: Define the Variables
Let the smaller odd number be represented as \( n \). Since we are looking for consecutive odd numbers, the next consecutive odd number can be expressed as \( n + 2 \).

### Step 2: Set Up the Equation
According to the problem, the sum of these two consecutive odd numbers is 36. Therefore, we can write the equation:
\[ n + (n + 2) = 36 \]

### Step 3: Simplify the Equation
Now, simplify the left side of the equation:
\[ n + n + 2 = 36 \]
This simplifies to:
\[ 2n + 2 = 36 \]

### Step 4: Isolate the Variable
Next, we need to isolate \( n \). Start by subtracting 2 from both sides:
\[ 2n = 36 - 2 \]
This simplifies to:
\[ 2n = 34 \]

### Step 5: Solve for \( n \)
Now, divide both sides by 2 to find the value of \( n \):
\[ n = \frac{34}{2} \]
This gives us:
\[ n = 17 \]

### Step 6: Find the Consecutive Odd Numbers
Now that we have \( n \), we can find the two consecutive odd numbers:
- The smaller odd number is \( n = 17 \).
- The next consecutive odd number is \( n + 2 = 19 \).

### Conclusion
Thus, the smaller of the two consecutive odd numbers is:
\[ \text{Smaller Odd Number} = 17 \]

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