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
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\n" ); document.write( "Given that they each received $208 dollars, how much does Sarah spend on clothes. \n" ); document.write( "

Algebra.Com's Answer #845881 by Edwin McCravy(20060) $\"\"$ $\"About$

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document.write( "There are more than 1 answer, because we are not given the number of sisters.\r\n" );
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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 N sisters, that doesn't mean she gives\r\n" );
document.write( "it all to them. She gives each of the siblings, including herself, (5/12)T/(N+1),\r\n" );
document.write( "which is 208.\r\n" );
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document.write( "So we have the Diophantine equation:\r\n" );
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document.write( "Here is the way I was taught to solve first degree Diophantine equations.\r\n" );
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document.write( "Write each number in terms of its nearest multiple of the smallest coefficient\r\n" );
document.write( "in absolute value. So write each 2496 as 2495+1 (because 2495 is the nearest\r\n" );
document.write( "multiple of 5.\r\n" );
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document.write( "Divide through by 5\r\n" );
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document.write( "Isolate the fraction terms:\r\n" );
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document.write( "The left side is an integer, so the right side is also an integer.\r\n" );
document.write( "Let that integer be A.\r\n" );
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document.write( ", the number of sisters\r\n" );
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document.write( "Substitute in\r\n" );
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document.write( "She spent  on clothes\r\n" );
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document.write( "A   Number of sisters  Spent on clothes\r\n" );
document.write( "          5A-1              520A\r\n" );
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document.write( "1           4                520\r\n" );
document.write( "2           9               1040\r\n" );
document.write( "3          14               1560\r\n" );
document.write( "4          19               2080\r\n" );
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document.write( "There are multiple answers.\r\n" );
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document.write( "Edwin

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