Question 193710
from  youngest  to  oldest,  let  ages  be  w,,x,,y,,z
,
1)  w+x+y+z  =  384
2)  y-w=14,  ,,y=(14+w)
3) x=(w+3)
4) z=( 20 + (y+w)/2 ),,,= (20+y/2+w/2)  = 20+(14+w)/2 +w/2= 20+7+w/2+w/2=  (27+w)
,
with  4  eqn  and 4  unknown,  we  can  solve
,
w+x+y+z = 384
(w)+(w+3)+(14+w)+(27+w) = 384
44+4w=384
4w=340
w=85  ********
substituting
x=(w+3)=88  ********
y= (14+w)=99******
z=(27+w)=112******
,
checking
85+88+99+112=384
384=384,,,,ok