令(x+y)/2=(y+z)/3=(x+z)/4=t,则
x+y=2t (1)
y+z=3t (2)
x+z=4t (3)
(1)+(2)+(3)
2(x+y+z)=9t
x+y+z=(9/2)t (4)
(4)-(2) x=(3/2)t
(4)-(3) y=(1/2)t
(4)-(1) z=(5/2)t
x=(3/2)t y=(1/2)t z=(5/2)t代入2x+4y+6z=120
3t+2t+15t=120
20t=120
t=6
x=(3/2)t=9 y=(1/2)t=3 z=(5/2)t=15
x=9 y=3 z=15