A four- digit integer,WXYZ,in which W X Y and Z,each represent a diffrent digit,is fprmed according to the following rules1 X=W+Y+Z2 W=Y+13 Z=W-5What is the four-digit integer?

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A four- digit integer,WXYZ,in which W X Y and Z,each represent a diffrent digit,is fprmed according to the following rules1 X=W+Y+Z2 W=Y+13 Z=W-5What is the four-digit integer?
A four- digit integer,WXYZ,in which W X Y and Z,each represent a diffrent digit,is fprmed according to the following rules
1 X=W+Y+Z
2 W=Y+1
3 Z=W-5
What is the four-digit integer?

A four- digit integer,WXYZ,in which W X Y and Z,each represent a diffrent digit,is fprmed according to the following rules1 X=W+Y+Z2 W=Y+13 Z=W-5What is the four-digit integer?
1-----------X=W+Y+Z
2-----------2 W=Y+1
3-----------3 Z=W-5
利用2和3式,将y和z化为w,得:
x=w+2w-1+1/3w-3/5w
化简:3x=10w-8
然后从x=1开始代入
因为题目说是整数,所以在代到x=4时就行
所以x=4 w=2 y=3 z=-1

求四位整数,每位分别为wxyz且都不同,并满足等式
因为 Z=W-5 >=0 所以W大于等于5
W=Y+1 所以Y大于等于4
X=W+Y+Z X也是一位数,W+Y大于等于9,所以Z等于0,之后类推
得5940

变换一下就是:
X=W+Y+Z
Y=W-1
Z=W-5
---
X=3W-6
因为WXYZ分别为一个整数,因此范围在0-9以内,可以用排除法,将0-9依次代入X=3W-6,返回去求剩余几个字母,算出来为整数的就是答案
例如假设X=0时,0=3W-6,W=2
W=Y+1——Y=1
Z=W-5——Z=-5,-5为负数不符合题目要求...

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变换一下就是:
X=W+Y+Z
Y=W-1
Z=W-5
---
X=3W-6
因为WXYZ分别为一个整数,因此范围在0-9以内,可以用排除法,将0-9依次代入X=3W-6,返回去求剩余几个字母,算出来为整数的就是答案
例如假设X=0时,0=3W-6,W=2
W=Y+1——Y=1
Z=W-5——Z=-5,-5为负数不符合题目要求,因此排除X=0
一楼正解,5940

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