SOLUTION: all variables are positive integers what is the value of each ? X + Y + Z + W = 34 X � Y � Z � W = 2240 X + X + W = Z

Question 979643: all variables are positive integers what is the value of each ?
X + Y + Z + W = 34
X � Y � Z � W = 2240
X + X + W = Z

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
X + Y + Z + W = 34
X � Y � Z � W = 2240
X + X + W = Z
The numbers are small, because 4 positive integers that add to 34 have an average of 8.5. The largest one can be is 31.
0,2,4 of the numbers can be odd.
One has to be evenly divisible by 5.
3X+Y+2W=34; substituting 3 into 1. Now, the largest number can be 29, but to allow the middle equation to be true, 28, 27, 26, and 25 can't work.
Look at factors of 2240
224*10
56*40
28*80
140*16=14*10*8*2. That adds to 34 and multiplies to 2240.
X=2
W=10
Z=14
Y=8
X+X+W=Z
2+2+10=14
ALL ADD TO 34
ALL MULTIPLY TO 2240.

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