document.write( "Question 80948: I need to know how old your three kids are. The product of their ages is 36.
\n" ); document.write( "The sum of their ages is the same as my house number. The younger two are twins.
\n" ); document.write( "How old are the kid's and what is my house number.\r
\n" ); document.write( "\n" ); document.write( "I think that the kids are 2 and 9 and the house number is 13 but I cannot figure out an equation. This didn't come from a textbook. It is an extra credit paper. \n" ); document.write( "

Algebra.Com's Answer #58091 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!
: I need to know how old your three kids are. The product of their ages is 36.
\n" ); document.write( "The sum of their ages is the same as my house number. The younger two are twins.
\n" ); document.write( "How old are the kid's and what is my house number.
\n" ); document.write( "I think that the kids are 2 and 9 and the house number is 13 but I cannot figure out an equation. This didn't come from a textbook. It is an extra credit paper.
\n" ); document.write( "

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document.write( "I suspect there is more than one solution.\r\n" );
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document.write( "Let the twins' age be t and the older child's age be c.\r\n" );
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document.write( ">>...The product of their ages is 36...<<\r\n" );
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document.write( "Translation into an equation: t x t x t = 36, or\r\n" );
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document.write( "t²c = 36\r\n" );
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document.write( "Solve for t.\r\n" );
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document.write( "Divide both sides by c\r\n" );
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document.write( "t² = 36/c\r\n" );
document.write( "    \r\n" );
document.write( "Take positive square roots of both sides\r\n" );
document.write( "       _ \r\n" );
document.write( "t = 6/Öc\r\n" );
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document.write( "The twins are younger than the older child, so\r\n" );
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document.write( "t < c \r\n" );
document.write( "                 _\r\n" );
document.write( "so substitute 6/Öc for t in that inequality\r\n" );
document.write( "   _\r\n" );
document.write( "6/Öc < c\r\n" );
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document.write( "Square both sides\r\n" );
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document.write( "36/c < c²\r\n" );
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document.write( "Multiply both sides by c, which is positive\r\n" );
document.write( "so the symbol of inequality will stay the same:\r\n" );
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document.write( "36 < c³\r\n" );
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document.write( "Take cube roots of both sides:\r\n" );
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document.write( "3.301927249 < c\r\n" );
document.write( "             _ \r\n" );
document.write( "Since t = 6/Öc,\r\n" );
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document.write( "vc must divide evenly ito 6\r\n" );
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document.write( "The only divisiors of 6 are 1, 2, 3, and 6, so\r\n" );
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document.write( "Öc must be 1, 2, 3 or 6, so\r\n" );
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document.write( "c must be 1, 4, 9, or 36 \r\n" );
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document.write( "But c must be greater than 3.301927249 so \r\n" );
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document.write( "c is either 4, 9, or 36, so\r\n" );
document.write( "             _     _       __  \r\n" );
document.write( "t must be 6/Ö4, 6/Ö9 or 6/Ö36, that is\r\n" );
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document.write( "t must be 6/2, 6/3, or 6/6, that is,  \r\n" );
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document.write( "t must be 3, 2, or 1\r\n" );
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document.write( "The three possibilities are\r\n" );
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document.write( "1. the twins are 3 and the older child is 4,\r\n" );
document.write( "   and the house number is 3 + 3 + 4 = 10\r\n" );
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document.write( "2. the twins are 2 and the older child is 9,\r\n" );
document.write( "   and the house number is 2 + 2 + 9 = 13, \r\n" );
document.write( "   (which was your solution)  \r\n" );
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document.write( "3. the twins are 1 and the older child is 36.\r\n" );
document.write( "   and the house number is 1 + 1 + 36 = 38 \r\n" );
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document.write( "You might rule out case 3, since 36 is a little old\r\n" );
document.write( "for a kid.  Also the mother of a 36-year-old would be\r\n" );
document.write( "too old to have 1-year-old twins, for she'd be past\r\n" );
document.write( "menopause!  Hahaha.  But the first two are both possible\r\n" );
document.write( "solutions.\r\n" );
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document.write( "Edwin

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