document.write( "Question 979643: all variables are positive integers what is the value of each ?
\n" ); document.write( "X + Y + Z + W = 34
\n" ); document.write( "X × Y × Z × W = 2240
\n" ); document.write( "X + X + W = Z
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Algebra.Com's Answer #600940 by Boreal(15235)\"\" \"About 
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X + Y + Z + W = 34
\n" ); document.write( "X × Y × Z × W = 2240
\n" ); document.write( "X + X + W = Z\r
\n" ); document.write( "\n" ); document.write( "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.
\n" ); document.write( "0,2,4 of the numbers can be odd.
\n" ); document.write( "One has to be evenly divisible by 5.
\n" ); document.write( "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.\r
\n" ); document.write( "\n" ); document.write( "Look at factors of 2240
\n" ); document.write( "224*10
\n" ); document.write( "56*40
\n" ); document.write( "28*80
\n" ); document.write( "140*16=14*10*8*2. That adds to 34 and multiplies to 2240.
\n" ); document.write( "X=2
\n" ); document.write( "W=10
\n" ); document.write( "Z=14
\n" ); document.write( "Y=8\r
\n" ); document.write( "\n" ); document.write( "X+X+W=Z
\n" ); document.write( "2+2+10=14
\n" ); document.write( "ALL ADD TO 34
\n" ); document.write( "ALL MULTIPLY TO 2240.
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