document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=31262>Question 31262</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0534373526/algebrahomeworkh>College Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> A group of friends decides to buy a vacation home for $120,000, sharing the cost equally. If they could find one more person to join them, each person's contribution would drop by $6,000. How many people are in the group?\r<BR>\n" );
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document.write( "Thank you so very much! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #17967 by </B><A HREF=/tutors/aboutme.mpl?userid=mukhopadhyay><B>mukhopadhyay(490)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mukhopadhyay><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=17967\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Assume that the group has x number of people<BR>\n" );
document.write( "Cost per head is 120,000/x<BR>\n" );
document.write( "Increasing the persons by one more will make the number of persons as (x+1)<BR>\n" );
document.write( "Cost per head will then be 120000/(x+1)<BR>\n" );
document.write( "As per the question, 120000/(x+1) = 120000/x - 6000<BR>\n" );
document.write( "=>(120000/x)-[120000/(x+1)]=6000<BR>\n" );
document.write( "=>120000[1/x - 1/(x+1)]=6000<BR>\n" );
document.write( "=>20[1/x - 1/(x+1)] = 1<BR>\n" );
document.write( "=>20[(x+1-x)/x(x+1)]=1<BR>\n" );
document.write( "=>20[1/x(x+1)]=1<BR>\n" );
document.write( "=>x(x+1)=20<BR>\n" );
document.write( "=>x^2+x-20=0<BR>\n" );
document.write( "=>(x+5)(x-4)=0<BR>\n" );
document.write( "=>x=-5 or x=4\r<BR>\n" );
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document.write( "Number of persons cannot be negative.  So, total number of people in the group is 4.<BR>\n" );
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