document.write( "Question 129610: During a recent cesus, a man was being interviewedby the census taker. When asked, he told the census taker that he had 3 children. When asked their ages the man replied, \"The product of their ages is 72. The sum of their ages is the same as my house number.\" The census taker ran to the front door, looked at the house number and returned saying \"I still cant tell!\" The man replied, Oh thats right! I forgot to tell youthe oldest one likes chocolate pudding.\" With That, the census taker wrote down the ages of the 3 children and left. How old are they? \n" ); document.write( "
Algebra.Com's Answer #94643 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
During a recent cesus, a man was being interviewedby the census taker. When asked, he told the census taker that he had 3 children. When asked their ages the man replied, \"The product of their ages is 72.
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document.write( "So their ages are one of these\r\n" );
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document.write( "1,1,72\r\n" );
document.write( "1,2,36\r\n" );
document.write( "1,3,24\r\n" );
document.write( "1,4,18\r\n" );
document.write( "1,6,12\r\n" );
document.write( "1,8,9\r\n" );
document.write( "2,2,18\r\n" );
document.write( "2,3,12\r\n" );
document.write( "2,4,9\r\n" );
document.write( "2,6,6\r\n" );
document.write( "3,3,8\r\n" );
document.write( "3,4,6\r\n" );
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document.write( "I know that the first three cases are ridiculous because children can't\r\n" );
document.write( "be 24, 36 or 72.  But this just shows that the problem didn't have to say\r\n" );
document.write( "they were children.  They could have just been any three people that live\r\n" );
document.write( "in the house with them.   \r\n" );
document.write( "

\n" ); document.write( "The sum of their ages is the same as my house number.\"
\n" ); document.write( "The census taker ran to the front door, looked at the house
\n" ); document.write( "number and returned saying \"I still cant tell!\"
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document.write( "So we find all the sums:\r\n" );
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document.write( "1+1+72 = 74\r\n" );
document.write( "1+2+36 = 39\r\n" );
document.write( "1+3+24 = 28\r\n" );
document.write( "1+4+18 = 23\r\n" );
document.write( "1+6+12 = 19\r\n" );
document.write( "1+8+9 = 18\r\n" );
document.write( "2+2+18 = 22\r\n" );
document.write( "2+3+12 = 17\r\n" );
document.write( "2+4+9 = 15\r\n" );
document.write( "2+6+6 = 14\r\n" );
document.write( "3+3+8 = 14\r\n" );
document.write( "3+4+6 = 13\r\n" );
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document.write( "So we see from the list he could have told their ages if\r\n" );
document.write( "the sum of their ages (and therefore the house number) had been \r\n" );
document.write( "anything other than 14 because 14 is the only sum that occurs \r\n" );
document.write( "more than once in the list.  So he has narrowed it down \r\n" );
document.write( "to two possibilities:\r\n" );
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document.write( "2, 6, and 6 \r\n" );
document.write( "3, 3, and 8 \r\n" );
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document.write( "an OLDER set of twins, and a YOUNGER set of twins.\r\n" );
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\n" ); document.write( "The man replied, Oh that's right! I forgot to tell you the oldest one likes chocolate pudding.\"
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document.write( "Well, the chocolate pudding had nothing to do with it. :-)  But\r\n" );
document.write( "the fact that there is an OLDEST one does. It rules out the case\r\n" );
document.write( "of their ages being 2, 6, and 6 for then the oldest two would be\r\n" );
document.write( "twins and neither would be the OLDEST, so there couldn't have been\r\n" );
document.write( "an OLDEST.\r\n" );
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document.write( "So he now knows that they are 3, 3, and 8.  \r\n" );
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document.write( "Edwin

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