The sum of three consecutive even numbers is 28 more than the average of these three numbers. Then the smallest of these three numbers is

Options

A. 6
B. 12
C. 14
D. 16

Answer

To solve the problem step by step, we will follow the reasoning provided in the video transcript.

### Step 1: Define the three consecutive even numbers
Let's denote the smallest of the three consecutive even numbers as \( n - 2 \), the middle number as \( n \), and the largest number as \( n + 2 \).

### Step 2: Calculate the sum of the three numbers
The sum of these three numbers can be expressed as:
\[ (n - 2) + n + (n + 2) = 3n \]

### Step 3: Calculate the average of the three numbers
The average of these three numbers is given by:
\[ \text{Average} = \frac{\text{Sum}}{\text{Number of terms}} = \frac{3n}{3} = n \]

### Step 4: Set up the equation based on the problem statement
According to the problem, the sum of the three consecutive even numbers is 28 more than the average of these three numbers. This can be expressed as:
\[ 3n = n + 28 \]

### Step 5: Solve the equation
Now, we will solve the equation:
\[ 3n - n = 28 \]
\[ 2n = 28 \]
\[ n = 14 \]

### Step 6: Find the smallest of the three numbers
The smallest of the three consecutive even numbers is:
\[ n - 2 = 14 - 2 = 12 \]

Thus, the smallest of the three consecutive even numbers is **12**.

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