已知3分之X+2Y=4分之Y+3Z=5分之Z+5X则X:Y:Z是多少
2个回答

你好!

设 (x+2y)/3 = (y+3z)/4 = (z+5x)/5 = k

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