document.write( "Question 877443: In the adjacent sum, A, B, C are consecutive digits. In the third row A,B,C appear in same order. Find A, B, C.\r
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Algebra.Com's Answer #529361 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Since A,B,C are consecutive digits,\r\n" );
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document.write( "B=A+1, C=A+2\r\n" );
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document.write( "Let the digits of the third number be \r\n" );
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document.write( "A+x, A+y and A+z where {x,y,z} = {0,1,2}\r\n" );
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document.write( "[[100A+10(A+1)+(A+2)]+[100(A+2)+10(A+1)+A]+[100(A+x)+10(A+y)+(A+z) = 1242\r\n" );
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document.write( "That simplifies to\r\n" );
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document.write( "333A+100x+10y+z = 1020\r\n" );
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document.write( "     100x+10y+z = 1020-333A\r\n" );
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document.write( "The left side is the number \"xyz\"\r\n" );
document.write( "and it is a 2 or 3 digit number with \r\n" );
document.write( "digits {0,1,2} in some order.\r\n" );
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document.write( "The least it could be is 012, or 12, and the most it could be is 210\r\n" );
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document.write( "So    \"12+%3C=+1020-333A+%3C=+210\"\r\n" );
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document.write( "Subtract 1020 from all three sides:\r\n" );
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document.write( "      \"-1008+%3C=+-333A+%3C=+-810\"\r\n" );
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document.write( "Divide all three sides by -333\r\n" );
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document.write( "      \"3%2610%2F333+%3E=+A+%3E=+2%2616%2F37\" \r\n" );
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document.write( "The only integer between those values is A = 3\r\n" );
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document.write( "Thus A = 3\r\n" );
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document.write( "Substituting in\r\n" );
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document.write( "100x+10y+z = 1020-333A\r\n" );
document.write( "100x+10y+z = 1020-333(3)\r\n" );
document.write( "100x+10y+z = 1020-999\r\n" );
document.write( "100x+10y+z = 21\r\n" );
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document.write( "So x must be 0 otherwise the left side will be more than 21\r\n" );
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document.write( "100(0)+10y+z = 21\r\n" );
document.write( "       10y+z = 21\r\n" );
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document.write( "So the only way that can be true is for y=2  and z=1\r\n" );
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document.write( "So the digits in the third row are\r\n" );
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document.write( "A+x, A+y, A+z or 3+0, 3+2, 3+1 or 3, 5, 4\r\n" );
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document.write( "   A B C                  3 4 5\r\n" );
document.write( "+  C B A               +  5 4 3\r\n" );
document.write( "+  - - -               +  3 5 4\r\n" );
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document.write( " 1 2 4 2                1 2 4 2\r\n" );
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document.write( "Edwin
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