document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=505738>Question 505738</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A group of women decided to contribute equal amounts toward obtaining a speaker for a book review. If there were 10 more women, each would have paid $2 less. However, if there were 5 less women, each would have paid $2 more. How many women were in the group and how much was the speaker paid? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #339972 by </B><A HREF=/tutors/aboutme.mpl?userid=Maths68><B>Maths68(1474)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Maths68><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=Maths68><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=339972\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let<BR>\n" );
document.write( "Initially<BR>\n" );
document.write( "Total number woman=x<BR>\n" );
document.write( "Contribution for one woman =  y<BR>\n" );
document.write( "Total amount = x*y=xy<BR>\n" );
document.write( "---------------------------------------------------------------------------<BR>\n" );
document.write( "After 5 did not join the group<BR>\n" );
document.write( "Remaining women = x-5<BR>\n" );
document.write( "Contribution for one woman = y+2<BR>\n" );
document.write( "Total amount  = (y+2)*(x-5)\r<BR>\n" );
document.write( "\n" );
document.write( "Total amount = Total amount after 5 did not join the group<BR>\n" );
document.write( "xy=(y+2)*(x-5)<BR>\n" );
document.write( "xy=xy-5y+2x-10<BR>\n" );
document.write( "0=-5y+2x-10<BR>\n" );
document.write( "2x-5y-10=0<BR>\n" );
document.write( "2x-5y=10…………..(1)<BR>\n" );
document.write( "-----------------------------------------------------------------------------<BR>\n" );
document.write( "After 10 more  join the group<BR>\n" );
document.write( "Total  women = x+10<BR>\n" );
document.write( "Contribution for one woman = y-2<BR>\n" );
document.write( "Total amount  = (y-2)*(x+10)<BR>\n" );
document.write( "Total amount = Total amount after 10 more join the group<BR>\n" );
document.write( "xy=(y-2)*(x+10)<BR>\n" );
document.write( "xy=xy+10y-2x-20<BR>\n" );
document.write( "0=10y-2x-20<BR>\n" );
document.write( "-2x+10y-20=0<BR>\n" );
document.write( "-2x+10y=20 ……………..(2)<BR>\n" );
document.write( "-----------------------------------------------------------------------------<BR>\n" );
document.write( "Add (1) and (2)<BR>\n" );
document.write( "2x-5y=10…………..(1)<BR>\n" );
document.write( "-2x+10y=20 ……………..(2)<BR>\n" );
document.write( "-----------<BR>\n" );
document.write( "5y=30<BR>\n" );
document.write( "Divide by 5 both sides of the equation<BR>\n" );
document.write( "5y/5=30/5<BR>\n" );
document.write( "y=6<BR>\n" );
document.write( "-------------------------------------------------------------------------------<BR>\n" );
document.write( "Put the value of y in (1)<BR>\n" );
document.write( "2x-5y=10…………..(1)<BR>\n" );
document.write( "2x-5(6)=10<BR>\n" );
document.write( "2x-30=10<BR>\n" );
document.write( "2x=10+30<BR>\n" );
document.write( "2x=40<BR>\n" );
document.write( "Divide by 2 both sides of the equation<BR>\n" );
document.write( "2x/2=40/2<BR>\n" );
document.write( "x=20<BR>\n" );
document.write( "-------------------------------------------------------------------------------<BR>\n" );
document.write( "Total number woman=x = 20<BR>\n" );
document.write( "Total amount = xy=20*6=$120<BR>\n" );
document.write( "Intial contribution for one woman = 120/20 = 6\r<BR>\n" );
document.write( "\n" );
document.write( "After 5 did not join  remaining women = 20-5=15<BR>\n" );
document.write( "Contribution for one woman = 120/15 = 8\r<BR>\n" );
document.write( "\n" );
document.write( " <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );