document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=472802>Question 472802</A>: <I><SPAN STYLE=\"word-break: break-all;\"> here is my question- a group of women decide 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? \r<BR>\n" );
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document.write( "If you can, could you also show me how you did it? <BR>\n" );
document.write( "Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #324147 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=324147\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a group of women decide 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?<BR>\n" );
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document.write( "Let A = the amount the speaker was paid<BR>\n" );
document.write( "Let a = the amount each woman paid<BR>\n" );
document.write( "Let n = the number of women in the group<BR>\n" );
document.write( "Given the information above, we can write the following 3 equations:<BR>\n" );
document.write( "A = na<BR>\n" );
document.write( "A = (n+10)(a-2)<BR>\n" );
document.write( "A = (n-5)(a+2)<BR>\n" );
document.write( "Since the LHS's are equal we can write:<BR>\n" );
document.write( "na = (n+10)(a-2) [1]<BR>\n" );
document.write( "na = (n-5)(a+2)  [2]<BR>\n" );
document.write( "Now we are left with 2 equations and 2 unknowns.  Solving for a in [1] gives:<BR>\n" );
document.write( "na = na - 2n + 10a - 20 -> 2n = 10a - 20 -> n = 5a - 10<BR>\n" );
document.write( "Now simplify [2] and substitute in this value for n:<BR>\n" );
document.write( "na = na + 2n - 5a - 10 -> 2n - 5a - 10 = 0 -> 2(5a - 10) - 5a - 10 = 0<BR>\n" );
document.write( "Solving for a gives:<BR>\n" );
document.write( "10a - 20 - 5a - 10 = 0<BR>\n" );
document.write( "5a - 30 = 0<BR>\n" );
document.write( "This gives a = 6<BR>\n" );
document.write( "Therefore, n = 5*6 - 10 -> n = 20<BR>\n" );
document.write( "So there were 20 women in the group and the speaker was paid 20*6 = $120\r<BR>\n" );
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