Question

已知：a+b/10=b+c/11=c+a/15，求a：b：c的值

Answer 1

因(a+b)/10=(b+c)/11=(c+a)/15
所以2(a+b+c)/(10+11+15)=(a+b)/10=(b+c)/11=(c+a)/15
(a+b+c)/18=(a+b)/10................(1)
(a+b+c)/18=(b+c)/11................(2)
(a+b+c)/18=(c+a)/15................(3)
解(1).(2).(3)得:
a+b=5/4*c.............................(4)
b+c=11/7*a...........................(5)
a+c=5b.....................................(6)
(6)-(5)得
a-b=5b-11/7*a.
3a=7b
a:b=7:3
(4)-(6)得
b-c=5/4*c-5b.
8b=3c
b:c=3:8
所以,a:b:c=7:3:8