x I----------------I 2x/5 I
y I----------------Iy/7I
z I----------------I z/3 I
x + y + z = 312
x*(1 - 2/5) = y*(1 - 1/7) = z*(1 - 1/3).
3x/5 = 6y/7 = 2z/3
6x/10 = 6y/7 = 6z/9 = 6*(x+y+z)/(10+7+9) = 6*312/26 = 72
6x/10 = 72
x=120.
6y/7 = 72
y=84
6z/9 = 72
z=108