Here's a way to do this with one variable only.
Let the son's age =x, the daughter's age = 2x, and the mother's age = 4x
And we have that in 22 years, the son wll be half as old as the mother......thus.....
2(x + 22) = 4x + 22
2x + 44 = 4x + 22
22 = 2x
x = 11 and that's the son's age
2x = 22 and that's the daughter's age
