document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189395>Question 1189395</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this problem!!\r<BR>\n" );
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document.write( ": A book dealer has books in store of which 1/5 were hardcover books . the dealer sold 2/3 of the books , including 3/4 of the hardcover books . what fraction of the unsold books were hardcover books?? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #820745 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=820745\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = the number of books the dealer had.<BR>\n" );
document.write( "let h = the number of hard cover books.\r<BR>\n" );
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document.write( "1/5 of the books were hard cover.<BR>\n" );
document.write( "therefore:<BR>\n" );
document.write( "h = 1/5 * x\r<BR>\n" );
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document.write( "the dealer sold 2/3 of the books that included 3/4 of the hard cover books.\r<BR>\n" );
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document.write( "this means the dealer sold 3/4 * h.\r<BR>\n" );
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document.write( "this means the dealer did not sell 1/4 * h.\r<BR>\n" );
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document.write( "the fraction of the books that were not sold = 1/3 * x.\r<BR>\n" );
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document.write( "the ratio of the number of hard cover books that were not sold to the number of books that were not sold is (1/4 * h) / (1/3 * x).\r<BR>\n" );
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document.write( "since h = 1/5 * x, the ratio becomes (1/4 * 1/5 * x) / (1/3 * x).\r<BR>\n" );
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document.write( "that becomes (1/20 * x) / (1/3 * x).\r<BR>\n" );
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document.write( "that becomes (1/20) / (1/3) which is equal to (1/20) * 3 which is equal to 3/20.\r<BR>\n" );
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document.write( "the fraction of the unsold books that were hard cover was 3/20.\r<BR>\n" );
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document.write( "to test this out, i created an example.<BR>\n" );
document.write( "in the example, i assumed the total number of books was 120.<BR>\n" );
document.write( "since the number of hard cover books was 1/5 * the total number of books, then the number of hard cover books was 24.\r<BR>\n" );
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document.write( "2/3 of the books were sold, including 3/4 of the hard cover books.\r<BR>\n" );
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document.write( "what was sold was:<BR>\n" );
document.write( "2/3 * 120 = 80 total books.<BR>\n" );
document.write( "this included 3/4 * 24 = 18 hard cover books.\r<BR>\n" );
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document.write( "what was not sold was:<BR>\n" );
document.write( "1/3 * 120 = 40 total books.<BR>\n" );
document.write( "this included 1/4 * 24 = 6 hard cover books.\r<BR>\n" );
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document.write( "the ratio of unsold hard cover books to unsold books was 6/40 = 3/20.\r<BR>\n" );
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document.write( "this confirms the fraction is correct.\r<BR>\n" );
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document.write( "your solution is that the fraction of unsold books that were hard cover books is 3/20.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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