Question

已知x+y/2=y+z/3=x+z/4,且2x+4y+6z=120,求x、y、z的值.

Answer 1

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