Find three consecutive even integers whose sum is 200 more than the smallest integer.

X, X+2, X+4 ARE THE 3 POSITIVE CONSECUTIVE INTEGERS.
X(X+2)=8+38(X+4)
X^2+2X=8+38X+152
X^2+2X-38X-8-152=0
X^2-36X-160=0
(X-40)(X+4)=0

X-40=0
X=40 ANSWER FOR THE FIRST INTEGER.
40+2=42 FOR THE SECOND INTEGER.

Let the 3  even numbers be 2x, 2x + 2 and 2x + 4, so we have:-

2x + 2x + 2 + 2x + 4 = 2x + 200

4x = 194

x = 48.5

2x = 97 

The question wants even numbers so there is no answer to this 

the numbers 97,99 and 101  fit the equation but these are odd numbers.