The sum of three consecutive even positive numbers is 28 more than the average of three numbers, the smallest number is equal to :

Question

Accepted Answer

To solve the problem, let's denote the three consecutive even positive numbers as $ x $, $ x+2 $, and $ x+4 $.

1. **Sum of the numbers**:  
   The sum of these numbers is:  
   $$ x + (x+2) + (x+4) = 3x + 6 $$

2. **Average of the numbers**:  
   The average of these numbers is:  
   $$ \frac{x + (x+2) + (x+4)}{3} = \frac{3x + 6}{3} = x + 2 $$

3. **Condition given in the problem**:  
   The sum of the numbers is 28 more than the average of the numbers:  
   $$ 3x + 6 = (x + 2) + 28 $$

4. **Solving the equation**:  
   Simplify the equation:  
   $$ 3x + 6 = x + 30 $$  
   Subtract $ x $ from both sides:  
   $$ 2x + 6 = 30 $$  
   Subtract 6 from both sides:  
   $$ 2x = 24 $$  
   Divide by 2:  
   $$ x = 12 $$

Thus, the smallest number is 12, which corresponds to Option 2.

**Explanation for why other options are incorrect:**

- **Option 1 (6)**:  
  If the smallest number were 6, the numbers would be 6, 8, and 10. The sum would be 24, and the average would be 8. The sum is not 28 more than the average (24 ≠ 8 + 28).

- **Option 3 (14)**:  
  If the smallest number were 14, the numbers would be 14, 16, and 18. The sum would be 48, and the average would be 16. The sum is not 28 more than the average (48 ≠ 16 + 28).

- **Option 4 (16)**:  
  If the smallest number were 16, the numbers would be 16, 18, and 20. The sum would be 54, and the average would be 18. The sum is not 28 more than the average (54 ≠ 18 + 28).

Therefore, Option 2 is the only correct answer, as it satisfies the condition given in the problem.