document.write( "Question 631954: find 2 numbers that are 13 times the sum of their digits. \n" ); document.write( "
Algebra.Com's Answer #397949 by Edwin McCravy(20086)\"\" \"About 
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document.write( "It could be 0, because the sum of its digit is 0 and 0 is 13x0.\r\n" );
document.write( "But that's stretching it a little. 0 is the only 1-digit number\r\n" );
document.write( "that could be a solution because no other digit is a multiple of 13.\r\n" );
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document.write( "It couldn't be a 2-digit number because the only 2-digit \r\n" );
document.write( "multiples of 13 are 13,26,39,52,65,78,91 and none of those \r\n" );
document.write( "are 13 times their sum of digits.\r\n" );
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document.write( "It can't be a 4 digit number or larger because the largest\r\n" );
document.write( "4-digit number 9999 has sum of digits of only 36, and 36x13\r\n" );
document.write( "is only 468, not a 4-digit number.  \r\n" );
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document.write( "Therefore it has to be a three digit number.\r\n" );
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document.write( "Let h = its hundreds digit\r\n" );
document.write( "Let t = its tens digit\r\n" );
document.write( "Let u = its units digit\r\n" );
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document.write( "100h+10t+u = 13(h+t+u)\r\n" );
document.write( "100h+10t+u = 13h + 13t + 13u\r\n" );
document.write( "       87h = 3t + 12u\r\n" );
document.write( "       29h = t + 4u\r\n" );
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document.write( "The largest t + 4u could be would be when t and u are both 9.\r\n" );
document.write( "making t + 4u = 9 + 4(9) = 45. thus\r\n" );
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document.write( "       29h <= 45\r\n" );
document.write( "         h <= \"1%2616%2F29\"\r\n" );
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document.write( "h can only be 1, and 29h = t + 4u becomes\r\n" );
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document.write( "        29 = t + 4u\r\n" );
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document.write( "Solving for t\r\n" );
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document.write( "     29 - 4u  = t\r\n" );
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document.write( "      -1 < t < 10\r\n" );
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document.write( "   -1 < 29 - 4u < 10\r\n" );
document.write( "  -30 <   -4u   < -19\r\n" );
document.write( "   30 >    4u   >  19\r\n" );
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document.write( "Divide through by 4\r\n" );
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document.write( "   7.5 > u > 4.75\r\n" );
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document.write( "Therefore u is 5, 6 or 7, the only digits in that interval.\r\n" );
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document.write( "If u = 5, substitute in\r\n" );
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document.write( "29 - 4u  = t\r\n" );
document.write( "29 - 4(5) = t\r\n" );
document.write( "29 - 20 = t\r\n" );
document.write( "      9 = t\r\n" );
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document.write( "So one solution is h=1, t=9, u=5, or the number 195\r\n" );
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document.write( "If u = 6, substitute in\r\n" );
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document.write( "29 - 4u  = t\r\n" );
document.write( "29 - 4(6) = t\r\n" );
document.write( "29 - 24 = t\r\n" );
document.write( "      5 = t\r\n" );
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document.write( "Another solution is h=1, t=5, u=6, or the number 156 \r\n" );
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document.write( "If u = 7, substitute in\r\n" );
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document.write( "29 - 4u  = t\r\n" );
document.write( "29 - 4(7) = t\r\n" );
document.write( "29 - 28 = t\r\n" );
document.write( "      1 = t\r\n" );
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document.write( "Another solution is h=1, t=1, u=7, or the number 117\r\n" );
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document.write( "There are three solutions 117, 156, and 195.  And you might\r\n" );
document.write( "mention that 0 could also be considered as a solution, but it's \r\n" );
document.write( "a little far-fetched.\r\n" );
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document.write( "Edwin

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