Find three consecutive even numbers whose sum is `234`.

Options

A. `76,78,80`
B. `80,82,84`
C. `74,76,78`
D. None

Answer

To find three consecutive even numbers whose sum is 234, we can follow these steps:

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

### Step 2: Write the Next Two Even Numbers
Since even numbers are spaced by 2, the next two consecutive even numbers can be expressed as:
- Second even number: \( x + 2 \)
- Third even number: \( x + 4 \)

### Step 3: Set Up the Equation
According to the problem, the sum of these three consecutive even numbers is equal to 234. Therefore, we can write the equation:
\[ x + (x + 2) + (x + 4) = 234 \]

### Step 4: Simplify the Equation
Now, simplify the left side of the equation:
\[ x + x + 2 + x + 4 = 234 \]
Combine like terms:
\[ 3x + 6 = 234 \]

### Step 5: Solve for \( x \)
Next, isolate \( x \) by first subtracting 6 from both sides:
\[ 3x = 234 - 6 \]
\[ 3x = 228 \]
Now, divide both sides by 3:
\[ x = \frac{228}{3} \]
\[ x = 76 \]

### Step 6: Find the Three Consecutive Even Numbers
Now that we have \( x \), we can find the three consecutive even numbers:
- First number: \( x = 76 \)
- Second number: \( x + 2 = 76 + 2 = 78 \)
- Third number: \( x + 4 = 76 + 4 = 80 \)

### Final Answer
The three consecutive even numbers are **76, 78, and 80**.

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