你好!
设 (x+2y)/3 = (y+3z)/4 = (z+5x)/5 = k
则
x+2y = 3k
y+3z = 4k
z+5x = 5k
解方程组得
x=25k/31
y=34k/31
z=30k/31
故x：y：z=25：34：30
已经验算过了,绝对正确!
还可以这么做
x+2y = 3k ①
y+3z = 4k ②
z+5x = 5k ③
① - 2*② 得 x - 6z = - 5k
除以③得 (x - 6z)/(z+5x) = - 1
x - 6z = -z - 5x
6x = 5z
x/z = 5/6
② - 3*③得 y-15x = -11k
除以①得 (y-15x)/(x+2y) = -11/3
3y - 45x = - 11x - 22y
25y = 34x
x/y = 25/34
又 x/z = 5/6 = 25/30
所以 x：y：z = 25：34：30