let x be the age of youngest sibling.
x= 22- 2-x - 3x
x+3x+x = 22 - 2
5x=20
x= 20/5
x=4
now that we know the youngest sibling is 4 years old. We can calculate the middle and the oldest.
Middle: 4+2=6 years old
Oldest= 3*4=12 years old
check answer: 12+6+4
=22