The sum of three consecutive even numbers is 10 more then the first of these numbers. What is the greatest number

Options

A. (a) 6
B. (b) 8
C. (c) 9
D. (d) 12

Answer

To solve the problem, we will follow these steps:

### Step 1: Define the Variables
Let the smallest of the three consecutive even numbers be represented by \( x \).

### Step 2: Express the Consecutive Even Numbers
The three consecutive even numbers can be expressed as:
- First number: \( x \)
- Second number: \( x + 2 \)
- Third number: \( x + 4 \)

### Step 3: Set Up the Equation
According to the problem, the sum of these three numbers is 10 more than the first number. Therefore, we can write the equation as:
\[ x + (x + 2) + (x + 4) = x + 10 \]

### Step 4: Simplify the Equation
Now, simplify the left side of the equation:
\[ x + x + 2 + x + 4 = x + 10 \]
This simplifies to:
\[ 3x + 6 = x + 10 \]

### Step 5: Solve for \( x \)
Next, we will isolate \( x \) by subtracting \( x \) from both sides:
\[ 3x + 6 - x = 10 \]
This simplifies to:
\[ 2x + 6 = 10 \]
Now, subtract 6 from both sides:
\[ 2x = 4 \]
Finally, divide by 2:
\[ x = 2 \]

### Step 6: Find the Greatest Number
Now that we have \( x \), we can find the three consecutive even numbers:
- First number: \( x = 2 \)
- Second number: \( x + 2 = 4 \)
- Third number: \( x + 4 = 6 \)

Thus, the greatest number is:
\[ \text{Greatest number} = x + 4 = 6 \]

### Final Answer
The greatest number is **6**.

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