Let's call the three consecutive even integers x, x + 2, and x + 4. These integers are consecutive because the difference between each pair is 2 (since even numbers are 2 apart).
Now, we're given that three times the smallest number is 28 more than the sum of these numbers. So, we can write an equation:
3x = (x + (x + 2) + (x + 4)) + 28
Now, let's solve for x:
3x = 3x + 6 + 28
To isolate x, we can subtract 3x from both sides:
0 = 6 + 28
There's no solution to this equation because it implies that 0 is equal to a positive number (6 + 28), which is not possible.
This means that there are no three consecutive even integers that satisfy the given condition. The problem might have been stated incorrectly or there might be a typo in the numbers.