If sum of six consecutive odd numbers is 168, then find the largest of these numbers.

Options

A. 23
B. 27
C. 31
D. 33

Answer

To find the largest of six consecutive odd numbers that sum up to 168, we can follow these steps:

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

### Step 2: Write the six consecutive odd numbers
The six consecutive odd numbers can be expressed as:
- First number: \( x \)
- Second number: \( x + 2 \)
- Third number: \( x + 4 \)
- Fourth number: \( x + 6 \)
- Fifth number: \( x + 8 \)
- Sixth number: \( x + 10 \)

### Step 3: Set up the equation for the sum
The sum of these six consecutive odd numbers is given by:
\[ x + (x + 2) + (x + 4) + (x + 6) + (x + 8) + (x + 10) = 168 \]

### Step 4: Simplify the equation
Combine like terms:
\[ 6x + (2 + 4 + 6 + 8 + 10) = 168 \]
Calculating the sum of constants:
\[ 2 + 4 + 6 + 8 + 10 = 30 \]
So, the equation becomes:
\[ 6x + 30 = 168 \]

### Step 5: Solve for \( x \)
Subtract 30 from both sides:
\[ 6x = 168 - 30 \]
\[ 6x = 138 \]
Now, divide both sides by 6:
\[ x = \frac{138}{6} = 23 \]

### Step 6: Find the largest odd number
The largest of the six consecutive odd numbers is:
\[ x + 10 = 23 + 10 = 33 \]

### Final Answer
The largest of these six consecutive odd numbers is **33**.

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