Three consecutive even integers exist such that when the sum of the smallest and middle-valued integers is subtracted from the largest integer, the result is −22. What are the three integers?

Answer 1

Let x = smallest of 3 even integers.

Then x+2 represents the middle integer

And x+4 represents the largest.

The sum of the smallest and middle is x + x+2 = 2x+2. That is subtracted from the largest, giving a result of -22:

(x+4) - (2x+2) = -22

x+4 - 2x -2 = -22

-x +2 = -22

-x = -24

x=24 (which is the smallest and indeed even)

x+2 = 26

x+4 = 28.

Check:

Sum of the 1st two is 50 (24+26).

28 - 50 = -22.