document.write( "Question 210031: wht is the solution of, a two digit number is four times the sum of its digits and thrice the product of its digits. find the number. \n" ); document.write( "
Algebra.Com's Answer #158733 by Edwin McCravy(20056)\"\" \"About 
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what is the solution of, a two digit number is four times the sum of its digits and thrice the product of its digits. find the number.
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document.write( "t = tens digit\r\n" );
document.write( "u = ones digit\r\n" );
document.write( "the two digit number = 10t+u\r\n" );
document.write( "t+u = sum of the digits\r\n" );
document.write( "tu = product of the digits\r\n" );
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\n" ); document.write( ">>...A two digit number is four times the sum of its digits...<<
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document.write( "So \r\n" );
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document.write( "\"10t%2Bu=4%28t%2Bu%29\"\r\n" );
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document.write( "Distribute on the right\r\n" );
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document.write( "\"10t%2Bu=4t%2B4u\"\r\n" );
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document.write( "Simplify:\r\n" );
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document.write( "\"6t=3u\"\r\n" );
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document.write( "Divide both sides by 3\r\n" );
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document.write( "\"2t=u\"\r\n" );
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\n" ); document.write( ">>...a two digit number is...thrice the product of its digits...<<
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document.write( "\"10t%2Bu=3%28tu%29\"\r\n" );
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document.write( "\"10t%2Bu=3tu\"\r\n" );
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document.write( "So we have this system of equations:\r\n" );
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document.write( "\"system%282t=u%2C10t%2Bu=3tu%29\"\r\n" );
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document.write( "Substitute \"2t\" for \"u\" in the 2nd equation\r\n" );
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document.write( "\"10t%2B%282t%29=3t%282t%29\"\r\n" );
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document.write( "\"10t%2B2t=6t%5E2\"\r\n" );
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document.write( "Combine terms on the left\r\n" );
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document.write( "\"12t=6t%5E2\"\r\n" );
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document.write( "Divide through by 6\r\n" );
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document.write( "\"2t=t%5E2\"\r\n" );
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document.write( "\"0=t%5E2-2t\"\r\n" );
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document.write( "\"t%5E2-2t=0\"\r\n" );
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document.write( "Factor out \"2\"\r\n" );
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document.write( "\"t%28t-2%29=0\"\r\n" );
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document.write( "Set each factor = 0\r\n" );
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document.write( "\"t=0\"   \"t-2=0\"\r\n" );
document.write( "            \"t=2\" \r\n" );
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document.write( "The ten's digit cannot be 0 for a 2-digit number.\r\n" );
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document.write( "So  \"t=2\"\r\n" );
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document.write( "Substitute that in \"2t=u\"\r\n" );
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document.write( "\"2t=u\"\r\n" );
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document.write( "\"2%282%29=u\"\r\n" );
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document.write( "\"4=u\"\r\n" );
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document.write( "So since \"t=2\" and \"u=4\",\r\n" );
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document.write( "The number is \"24\".\r\n" );
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document.write( "Checking:\r\n" );
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document.write( "The sum of the digits is 2+4 or 6\r\n" );
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document.write( "So 24 is 4 times the sum of its digits, \r\n" );
document.write( "because 24 is 4 times 6.\r\n" );
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document.write( "The product of the digits is 2×4 = 8\r\n" );
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document.write( "So 24 is thrice the product of its digits,\r\n" );
document.write( "because 24 is 3 times 8.\r\n" );
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document.write( "It checks.  \r\n" );
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document.write( "Edwin
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