document.write( "Question 1176795: If the man’s age is a 3-digit number, his age is equal to product of two
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Algebra.Com's Answer #804669 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Ikleyn gave us one possibility above, 144.  Let's see if we can find any\r\n" );
document.write( "others.\r\n" );
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\n" ); document.write( "the man’s age is a 3-digit number
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document.write( "So he's at least 100 years old!\r\n" );
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document.write( "Let h = the hundreds digit\r\n" );
document.write( "Let t = the tens digit\r\n" );
document.write( "Let u = the units or ones digit\r\n" );
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document.write( "His age = 100h+10t+u\r\n" );
document.write( "His age = htu(h+t+u)\r\n" );
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document.write( "      100h+10t+u = htu(h+t+u)\r\n" );
document.write( "(99+1)h+(9+1)t+u = htu(htu) \r\n" );
document.write( "    99h+h+9t+t+u = htu(h+t+u)\r\n" );
document.write( "    99h+9t+h+t+u = htu(h+t+u)\r\n" );
document.write( "          99h+9t = htu(h+t+u)-h-t-u\r\n" );
document.write( "        9(11h+t) = htu(h+t+u)-(h+t+u)\r\n" );
document.write( "        9(11h+t) = (h+t+u)(htu-1)\r\n" );
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document.write( "Pretty complicated.  Let's see if we can find any possibilities where he is\r\n" );
document.write( "less than 200 years old.  That would mean that h=1. Substituting:\r\n" );
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document.write( "        9(11+t) = (1+t+u)(tu-1)\r\n" );
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document.write( "Let's see if there are any possibilities where the 1st and 2nd factors on\r\n" );
document.write( "the left are equal respectively to the 1st and 2nd factors on the right.\r\n" );
document.write( "[That is not necessarily the case, but it could be, and trying it may lead\r\n" );
document.write( "to more answers].\r\n" );
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document.write( "   9 = 1+t+u, \r\n" );
document.write( "11+t = tu-1\r\n" );
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document.write( "Solve the first equation for u\r\n" );
document.write( " 8-t = u\r\n" );
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document.write( "Substitute in the second equation\r\n" );
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document.write( "      11+t = t(8-t)-1\r\n" );
document.write( "      11+t = 8t-t2-1\r\n" );
document.write( "  t2-7t+12 = 0    \r\n" );
document.write( "(t-4)(t-3) = 0\r\n" );
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document.write( "t-4=0; t-3=0\r\n" );
document.write( "  t=4;   t=3\r\n" );
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document.write( "If t=4, then 8-4 = u = 4.  That gives us 144, which Ikleyn found above.\r\n" );
document.write( "We don't know how she found it.  She just gave it.\r\n" );
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document.write( "But we also have another possibility for t=3\r\n" );
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document.write( "If t=3, then 8-3 = u = 5.  That gives us the age of 135, which Ikleyn did\r\n" );
document.write( "not give above. \r\n" );
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document.write( "The sum of the digits is 1+3+5 = 9 and the product is 1∙3∙5 = 15\r\n" );
document.write( "and 9∙15 = 135.\r\n" );
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document.write( "So now we know that two possibilities are that the man is 135 or 144.\r\n" );
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document.write( "I conjecture that 135 and 144 are the only possible solutions.\r\n" );
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document.write( "In either case, he is older than any person has ever known to have lived to\r\n" );
document.write( "be. Jeanne Louise Calment (1875-1997) from France lived to be 122+. She is\r\n" );
document.write( "listed in Guinness's world records as having the longest life span on\r\n" );
document.write( "record. \r\n" );
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document.write( "Edwin
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