document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=113462>Question 113462</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0618044302/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I know the answer, which is 97, because I found it in the back of the book, but I can't figure out how to solve the problem and I need to show work. Please help me with the steps. The question is:\r<BR>\n" );
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document.write( "Verna decided to sell her collection of paperback books. To Fred, she sold 2 books, and one fifth of what was left. Later to Joan she sold 6 books, and one fifth of what then remained. If she sold more books to Fred than to Joan what was the least possible number of books in her original collection? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #82544 by </B><A HREF=/tutors/aboutme.mpl?userid=rajagopalan><B>rajagopalan(174)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rajagopalan><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=rajagopalan><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=82544\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This a beautifully coined problem.<BR>\n" );
document.write( "Solution:<BR>\n" );
document.write( "First we find the solution for both Fred and Joan getting equal books.<BR>\n" );
document.write( "Then we add one more to Fred logically.<BR>\n" );
document.write( "Let the total number of books with Verna = x<BR>\n" );
document.write( "Books got by Fred = 2+((x-2)/5) ...first two plus one fifth of (x-2)<BR>\n" );
document.write( "Books got by Joan=6+((1/5)x(4/5(x-2)-6)...<BR>\n" );
document.write( "equaiting both<BR>\n" );
document.write( "1/5(4/5(x-2)-6)+6=((x-2)/5)+2<BR>\n" );
document.write( "multiply thro out by 5<BR>\n" );
document.write( "(4/5)(x-2)-6+20=x-2<BR>\n" );
document.write( "4(x-2)-30+100=5x-10  ...(again x5)<BR>\n" );
document.write( "4x-8-30+100=5x-10<BR>\n" );
document.write( "100-38=x<BR>\n" );
document.write( "72=x<BR>\n" );
document.write( "so with 72 books both get equal number of books (14 each) (2 + 70/5)=2+14=16<BR>\n" );
document.write( "so for Fred to get one more than Joan you have to add 5 more to Fred ( as denomoiantor is 5 in both cases.<BR>\n" );
document.write( "which leads to 2+(F/5)=21<BR>\n" );
document.write( "F=95<BR>\n" );
document.write( "and total books =95+2=97\r<BR>\n" );
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document.write( "Also you can use reduxio ad absurdem mehtod ie from  72 u keep on trying 77, 82 etc till u get a full number for Joan.\r<BR>\n" );
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document.write( "Answer 97 books\r<BR>\n" );
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document.write( " </SPAN>\n" );
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