The sum of four consecutive even numbers is 156. What is the value of thrice the largest even number?

Options

A. 124
B. 128
C. 136
D. None of these

Answer

To solve the problem, we need to find four consecutive even numbers whose sum is 156, and then calculate thrice the largest of these numbers. Let's break it down step by step.

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

### Step 2: Express the consecutive even numbers
The four consecutive even numbers can be expressed as:
- First even number: \( x \)
- Second even number: \( x + 2 \)
- Third even number: \( x + 4 \)
- Fourth even number: \( x + 6 \)

### Step 3: Set up the equation for their sum
According to the problem, the sum of these four consecutive even numbers is 156. Therefore, we can write the equation:
\[ x + (x + 2) + (x + 4) + (x + 6) = 156 \]

### Step 4: Simplify the equation
Combine like terms:
\[ x + x + 2 + x + 4 + x + 6 = 156 \]
This simplifies to:
\[ 4x + 12 = 156 \]

### Step 5: Solve for \( x \)
Now, isolate \( x \) by subtracting 12 from both sides:
\[ 4x = 156 - 12 \]
\[ 4x = 144 \]
Now, divide both sides by 4:
\[ x = \frac{144}{4} = 36 \]

### Step 6: Find the largest even number
Now that we have \( x \), we can find the largest even number:
\[ \text{Largest even number} = x + 6 = 36 + 6 = 42 \]

### Step 7: Calculate thrice the largest even number
To find thrice the largest even number:
\[ 3 \times 42 = 126 \]

### Final Answer
The value of thrice the largest even number is \( 126 \).

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