document.write( "Question 1206870: There were 5/7 as many red marbles as blue marbles in a jar. Dave took some blue marbles out of the jar and replaced them with the same number of red marbles. The number of red marbles became 5/9 of all the marbles in the jar. Which of the following is a possible number of blue marbles that were replaced? \n" ); document.write( "
Algebra.Com's Answer #844568 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Let R = the number of red marbles at the beginning.\r\n" );
document.write( "Let B = the number of blue marbles at the beginning,\r\n" );
document.write( "Let x = the the number of blue marbles exchanged for red marbles.  <--the answer\r\n" );
document.write( "There are R+B marbles at the beginning and at the end.  \r\n" );
document.write( "The given information \r\n" );
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document.write( "\"system%28R=expr%285%2F7%29%2AB%2C+R%2Bx=expr%285%2F9%29%28R%2BB%29%29\"\r\n" );
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document.write( "R, B, and x are all positive integers.\r\n" );
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document.write( "Since \"R=expr%285%2F7%29B\" B is a multiple of 7, say B=7p, where p is a positive\r\n" );
document.write( "integer.\r\n" );
document.write( "Then \"R=expr%285%2F7%29%287p%29\"\r\n" );
document.write( "or R=5p\r\n" );
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document.write( "\"R%2Bx=expr%285%2F9%29%28R%2BB%29%29\"\r\n" );
document.write( "\"5p%2Bx=expr%285%2F9%29%285p%2B7p%29\"\r\n" );
document.write( "\"5p%2Bx=expr%285%2F9%29%2812p%29\"\r\n" );
document.write( "\"5p%2Bx=expr%2820%2F3%29p\"\r\n" );
document.write( "\"15p%2B3x=20p\"\r\n" );
document.write( "\"3x=5p\"\r\n" );
document.write( "\"x=expr%285%2F3%29p\"\r\n" );
document.write( "So p must be a multiple of 3, say p=3n, where n is a positive integer.\r\n" );
document.write( "\"x=expr%285%2F3%29%283n%29\"\r\n" );
document.write( "\"x=5n\"\r\n" );
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document.write( "\"R=5p=5%283n%29=15n\"\r\n" );
document.write( "\"B=7p=7%283n%29=21n\"\r\n" );
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document.write( "So every solution in integers is of the form.\r\n" );
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document.write( "\"system%28B=21n%2CR=15n%2Cx=5n%29\"\r\n" );
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document.write( "You did not list the possible choices, but all you have to do is look for x\r\n" );
document.write( "being a multiple of 5.\r\n" );
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document.write( "Let's check the smallest possible solution where n=1. B=21, R=15, x=5
There were 5/7 as many red marbles as blue marbles in a jar.
That checks because 15=(5/7)(21). Now there are R+B=21+15=36 marbles total, before \r\n" );
document.write( "and after the swapping is done.
Dave took some blue marbles out of the jar and replaced them with
\n" ); document.write( "the same number of red marbles. The number of red marbles became 5/9
\n" ); document.write( "of all the marbles in the jar.
When 5 blues are swapped for reds there are 21-5=16 blues and 15+5=20 reds,\r\n" );
document.write( "and indeed, 20 = (5/9)(36). So that checks also.\r\n" );
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document.write( "Edwin
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