document.write( "Question 121311: 1.)A girl is one-third as old as her brother and 8 years younger than her sister.The sum of their ages is 38 years.How old is the girl?\r
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Algebra.Com's Answer #89031 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
1.)A girl is one-third as old as her brother and 8 years younger than her sister.The sum of their ages is 38 years. How old is the girl?
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document.write( "There is only one good way to learn to set up the equations\r\n" );
document.write( "for word problems. That way is to practice by \"cheating then\r\n" );
document.write( "checking\"!  That is:\r\n" );
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document.write( "1. Look up the answer in the back of the book.\r\n" );
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document.write( "2. Check that answer in the words to see WHY it is correct. \r\n" );
document.write( "Especially notice 'what equals to what'\r\n" );
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document.write( "3. Go through the SAME EXACT reasoning process, but using\r\n" );
document.write( "unknowns instead, and when you get to any place where you\r\n" );
document.write( "noticed that something was equal in the checking process,\r\n" );
document.write( "make an equation.  You simply \"check\" the problem using\r\n" );
document.write( "unknowns.\r\n" );
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document.write( "So you'll understand how to set up the problem. I'm going to\r\n" );
document.write( "first tell you their ages in advance.  Then we'll check them\r\n" );
document.write( "in the words.  Then I'll show you how to work the problem\r\n" );
document.write( "doing the same thing, that is, \"checking\" with unknowns\r\n" );
document.write( "instead of with knowns.\r\n" );
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document.write( "The girl is 6.\r\n" );
document.write( "Her brother is 18.\r\n" );
document.write( "Her sister is 14.\r\n" );
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document.write( "A girl is one-third as old as her brother\r\n" );
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document.write( " [and so the girl's age of 6 equals 1/3 of 18, which checks!] \r\n" );
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document.write( "   6 = 1/3(18)\r\n" );
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document.write( "and 8 years younger than her sister \r\n" );
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document.write( "[and so the girl's age of 6 equals her sister's age\r\n" );
document.write( "of 14 minus 8, which checks!].\r\n" );
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document.write( "    6 = 14 - 8 \r\n" );
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document.write( "The sum of their ages is 38 years. \r\n" );
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document.write( "[so 6+18+14 does equal to 38. That checks!]\r\n" );
document.write( "    \r\n" );
document.write( "   6 + 18 + 14 = 38\r\n" );
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document.write( "The girl is G.\r\n" );
document.write( "Her brother is B.\r\n" );
document.write( "Her sister is S.\r\n" );
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document.write( "A girl is one-third as old as her brother\r\n" );
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document.write( "[and so the girl's age of G equals 1/3 of B, \r\n" );
document.write( "which MUST check!] \r\n" );
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document.write( "          G = 1/3(B)\r\n" );
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document.write( "and 8 years younger than her sister \r\n" );
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document.write( "[and so the girl's age of G equals her sister's age\r\n" );
document.write( "of S minus 8, which MUST check!].\r\n" );
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document.write( "          G = S - 8 \r\n" );
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document.write( "The sum of their ages is 38 years.\r\n" );
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document.write( "[so G+B+S does equal to 38. That MUST check!]\r\n" );
document.write( "    \r\n" );
document.write( "  G + B + S = 38\r\n" );
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document.write( "So we have three equations which we can combine into \r\n" );
document.write( "one:\r\n" );
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document.write( "      G = 1/3(B)\r\n" );
document.write( "      G = S - 8\r\n" );
document.write( "  G + B + S = 38\r\n" );
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document.write( "Solve the first equation for B and get 3G = B\r\n" );
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document.write( "Solve the second equation for S and get G + 8 = S \r\n" );
document.write( "   \r\n" );
document.write( "Substitute 3G for B and G + 8 for S in the third\r\n" );
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document.write( "    G + B + S = 38\r\n" );
document.write( " G + 3G + G+8 = 38\r\n" );
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document.write( "Now solve that for G, and we get\r\n" );
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document.write( "       5G + 8 = 38\r\n" );
document.write( "           5G = 30\r\n" );
document.write( "            G = 6 \r\n" );
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document.write( "Then although they didn't happen to be \r\n" );
document.write( "asked for, although they COULD have been,\r\n" );
document.write( "we can get the brother's age from \r\n" );
document.write( "   \r\n" );
document.write( "           3G = B\r\n" );
document.write( "         3(6) = B\r\n" );
document.write( "           18 = B\r\n" );
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document.write( "and the sister's age from\r\n" );
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document.write( "        G + 8 = S\r\n" );
document.write( "        6 + 8 = S\r\n" );
document.write( "           14 = S\r\n" );
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document.write( "  ------------------------ \r\n" );
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\n" ); document.write( "2.)At present,the sum of the parent's ages is twice the sum of the children's ages. Five years ago,the sum of the parents ages was 4 times the sum of the childrens ages. Fifteen years hence,the sum of the parent's ages will be equal to the sum of the children's ages. How many children are there?
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document.write( "I'm sorry, but there is something wrong with this \r\n" );
document.write( "problem, because the answers come out that there \r\n" );
document.write( "are -4 children, the sum of the parents' ages\r\n" );
document.write( "is -180 and the sum of the children's ages is -90. \r\n" );
document.write( "That does check mathematically, but nobody is a \r\n" );
document.write( "negative number of years old and no parents have a \r\n" );
document.write( "negative number of children.  Please correct the \r\n" );
document.write( "problem and re-submit it.\r\n" );
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document.write( "Edwin

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