b/(a+c)=1/2,a/(b+c)=1/5 怎么得出a/(a+b+c)=1/6,b/(a+b+c)=1/3?

题目

b/(a+c)=1/2,a/(b+c)=1/5 怎么得出a/(a+b+c)=1/6,b/(a+b+c)=1/3?
b/(a+c)=1/2,a/(b+c)=1/5 怎么得出a/(a+b+c)=1/6,b/(a+b+c)=1/3?

答案

2b=a+c ...(1)
5a=b+c ...(2)
(1)-(2)得 2b-5a=a-b 6a=3b 2a=b ...(3)
上式代入(1)得 4a=a+c c=3a.(4)
所以a/(a+b+c)=a/(a+2a+3a)=1/6
b/(a+b+c) =2a/(a+2a+3a)=1/3