若a+2/3=b/4=c+5/6,且2a-b+3c=21.试求a:b:c.

问题描述:

a+2
3
b
4
c+5
6
,且2a-b+3c=21.试求a:b:c.

a+2
3
=
b
4
=
c+5
6
=k,
则a=3k-2,b=4k,c=6k-5,
所以,2(3k-2)-4k+3(6k-5)=21,
解得k=2,
所以a=6-2=4,b=8,c=7,
所以a:b:c=4:8:7.