document.write( "Question 1037857: A four-digit number with all different digits has the
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Algebra.Com's Answer #652516 by Edwin McCravy(20056)\"\" \"About 
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A four-digit number with all different digits has the
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document.write( "Let the number be \"ABCD\"\r\n" );
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document.write( "A+B+C+D=13\r\n" );
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document.write( "A = 2D or  D = \"A%2F2\"\r\n" );
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document.write( "C = B+1 or B = C-1\r\n" );
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document.write( "Substitute in A+B+C+D=13 and solve for A\r\n" );
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document.write( "\"A%2BC-1%2BC%2BA%2F2+=+13\"\r\n" );
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document.write( "\"A%2B2C%2BA%2F2+=+14\"\r\n" );
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document.write( "\"2A%2B4C%2BA+=+28\"\r\n" );
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document.write( "\"3A%2B4C+=+28\"\r\n" );
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document.write( "\"3A+=+28-4C\"\r\n" );
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document.write( "\"A+=+%2828-4C%29%2F3\"\r\n" );
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document.write( "All digits are between 0 and 9 inclusive\r\n" );
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document.write( "\"0+%3C=+A+%3C=+9\"\r\n" );
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document.write( "Substitute:\r\n" );
document.write( "\"0+%3C=+%2828-4C%29%2F3+%3C=+9\"\r\n" );
document.write( "Multiply through by 3\r\n" );
document.write( "\"0+%3C=+28-4C+%3C=+27\"\r\n" );
document.write( "Subtract 28 for all three sides\r\n" );
document.write( "\"-28+%3C=+-4C+%3C=+-1\"\r\n" );
document.write( "Divide through by -4 reversing inequalities\r\n" );
document.write( "\"7+%3E=+4C+%3E=+1\"\r\n" );
document.write( "\"1.75+%3E=+C+%3E=+0.25\"\r\n" );
document.write( "The only digit between 1.75 and 0.25 is 1 \r\n" );
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document.write( "Therefore C = 1 and since\r\n" );
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document.write( "\"A+=+%2828-4C%29%2F3\"\r\n" );
document.write( "\"A+=+%2828-4%281%29%29%2F3\"\r\n" );
document.write( "\"A+=+%2824%29%2F3\"\r\n" );
document.write( "A = 8\r\n" );
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document.write( "B = C-1 = 1-1 = 0 \r\n" );
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document.write( "D = \"A%2F2\" = \"8%2F2\" = 4\r\n" );
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document.write( "So \"ABCD\" = 8014\r\n" );
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document.write( "Edwin
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