The sum of four consecutive odd numbers is 328. Find the largest number.

Options

A. 85
B. 98
C. 79
D. 97

Answer

To solve the problem of finding the largest of four consecutive odd numbers whose sum is 328, we can follow these steps:

### Step 1: Define the Odd Numbers
Let the first odd number be represented as \( x \). Since we are dealing with consecutive odd numbers, the next three odd numbers can be expressed as:
- First odd number: \( x \)
- Second odd number: \( x + 2 \)
- Third odd number: \( x + 4 \)
- Fourth odd number: \( x + 6 \)

### Step 2: Set Up the Equation
According to the problem, the sum of these four consecutive odd numbers is 328. Therefore, we can write the equation:
\[ x + (x + 2) + (x + 4) + (x + 6) = 328 \]

### Step 3: Simplify the Equation
Now, simplify the left side of the equation:
\[ x + x + 2 + x + 4 + x + 6 = 328 \]
This simplifies to:
\[ 4x + 12 = 328 \]

### Step 4: Solve for \( x \)
Next, we need to isolate \( x \). First, subtract 12 from both sides:
\[ 4x = 328 - 12 \]
\[ 4x = 316 \]
Now, divide both sides by 4:
\[ x = \frac{316}{4} \]
\[ x = 79 \]

### Step 5: Find the Four Odd Numbers
Now that we have \( x \), we can find the four consecutive odd numbers:
- First odd number: \( 79 \)
- Second odd number: \( 79 + 2 = 81 \)
- Third odd number: \( 79 + 4 = 83 \)
- Fourth odd number: \( 79 + 6 = 85 \)

### Step 6: Identify the Largest Number
The largest of these four consecutive odd numbers is:
\[ 85 \]

### Final Answer
Thus, the largest number is **85**.

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