document.write( "Question 1202746: In a library, 40% of the books were fiction and the rest were non-fiction. When 875 books were borrowed, the number of fiction books became half of the original number and the number of non-fiction books were decreased by 25%.
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Algebra.Com's Answer #837832 by ikleyn(52786) $\"\"$ $\"About$

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\n" ); document.write( "In a library, 40% of the books were fiction and the rest were non-fiction.
\n" ); document.write( "When 875 books were borrowed, the number of fiction books became half of the original number
\n" ); document.write( "and the number of non-fiction books were decreased by 25%.
\n" ); document.write( "a) How many non-fiction books were borrowed?
\n" ); document.write( "b) How many fiction books were there at first?
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document.write( "Let x be the original number of books in the library.\r\n" );
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document.write( "According to the problem's description, there were 0.4x fiction books \r\n" );
document.write( "and 0.6x non-fiction books originally (the rest).\r\n" );
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document.write( "When 875 books were borrowed, the number of remaining fiction     books became half of 0.4x, i.e. 0.2x;\r\n" );
document.write( "                              the number of remaining non-fiction books became 0.75 of 0.6x, i.e. 0.75*0.6x = 0.45x.\r\n" );
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document.write( "So, when 875 were borrowed, the total of remaining books became 0.2x + 0.45x = 0.65x.\r\n" );
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document.write( "Obviously, this amount is equal to x-875, so we have this equation\r\n" );
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document.write( "    0.65x = x - 875.\r\n" );
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document.write( "Simplify and find x\r\n" );
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document.write( "    875 = x - 0.65x\r\n" );
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document.write( "    875 = 0.35x\r\n" );
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document.write( "      x =  = 2500.\r\n" );
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document.write( "Thus, originally there were 2500 books in the library.\r\n" );
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document.write( "Of them, the number of fiction     books was 0.4*2500 = 1000;    ANSWER to question b)\r\n" );
document.write( "         the number of non-fiction books was 0.6*2500 = 1500.\r\n" );
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document.write( "The number of non-fiction books borrowed was 25% of 1500, i.e. 0.25*1500 = 375.   ANSWER to question a)\r\n" );
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\n" ); document.write( "\n" ); document.write( "The solution is obtained using one single equation and one single unknown.\r
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