The sum of three consecutive even integers is 30 more than the smallest integer

Let's call the smallest of the three even integers ' T ' (for 'tiny')

The second even number is    T + 2.
The third even number is        T + 4.

Add up the 3 even numbers:  T + (T + 2) + (T + 4) = 3T + 6

This is 30 more than the smallest of the three.     

                                                3T + 6 = T + 30

Subtract  T  from each side:    2T + 6 =        30

Subtract  6  from each side:    2T       =         24

Divide each side by  2 :            T        =        12

The three consecutive even integers are  12,  14, and  16 .

Check:  12 + 14 + 16 = 42 .  By George, that's 30 more than 12 !