document.write( "Question 1207675: Hi
\n" ); document.write( "Sarah spent 3/8 of her allowance on food and 1/3 of the remainder on clothes. Then she shares the rest of her allowance equally with her sisters such that each of them received 1/12 of her total allowance. \r
\n" ); document.write( "\n" ); document.write( "How many sisters does she have.
\n" ); document.write( "Given that they each received $208 dollars, how much does Sarah spend on clothes. \n" ); document.write( "
Algebra.Com's Answer #845882 by ikleyn(52805)\"\" \"About 
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\n" ); document.write( "Sarah spent 3/8 of her allowance on food and 1/3 of the remainder on clothes.
\n" ); document.write( "Then she shares the rest of her allowance equally with her sisters such that
\n" ); document.write( "each of them received 1/12 of her total allowance.
\n" ); document.write( "How many sisters does she have.
\n" ); document.write( "Given that they each received $208 dollars, how much does Sarah spend on clothes.
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\n" ); document.write( "\n" ); document.write( "        The treatment of the problem by  Edwin is incorrect.\r
\n" ); document.write( "\n" ); document.write( "        It is incorrect,  because  Edwin ignored  (did not use)
\n" ); document.write( "        the condition that every sibling got  1/12  of the  Sarah's total allowance.\r
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\n" ); document.write( "\n" ); document.write( "        So,  in Edwin' solution this last condition was,  actually,  ignored.
\n" ); document.write( "        This brought  Edwin to  Diophantine equation,  while the true logic is much simpler.\r
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document.write( "Starts with T.\r\n" );
document.write( "Spends (3/8)T on food.  Has (5/8)T left.\r\n" );
document.write( "Spends (1/3)(5/8)T = (5/24)T on clothes. Has (5/8)T-(5/24)T = (5/12)T left.\r\n" );
document.write( "Shares equally with N sisters.\r\n" );
document.write( "Since it says she shares equally with sisters, that doesn't mean she gives\r\n" );
document.write( "it all to them. \r\n" );
document.write( "She gives each of the siblings, including herself, (1/12)T,\r\n" );
document.write( "which is 208 dollars.\r\n" );
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document.write( "So, to compute the number of sisters, including Sarah, we should divide (5/12)T by (1/12)T.\r\n" );
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document.write( "Obviously, the quotient is 5.  So, the number of sisters (including Sarah) is 5.\r\n" );
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document.write( "Also, from the analysis above,  (1/12)T = 208;  hence,  T = 208*12 = 2496 dollars.\r\n" );
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document.write( "The amount, which Sarah spent on clothes is (5/24)*2496 = 520 dollars.\r\n" );
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document.write( "ANSWER.  Sarah has 5-1 = 4 sisters.\r\n" );
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document.write( "         The amount Sarah spent on clothes was $520.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "Edwin's error is a typical error what mathematicians make when they solve simple problems:
\n" ); document.write( "they over-complicate them in their minds.\r
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