document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1184050>Question 1184050</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a swimming club, the ratio of th number of girls to the number of boys was 5:3. After 3 girls and 5 boys joined the club, the ratio became 7:5. How many girls were there in the club at first?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #814595 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=814595\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = number of girls.<BR>\n" );
document.write( "let y = number of boys.\r<BR>\n" );
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document.write( "original ratio is x/y = 5/3.\r<BR>\n" );
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document.write( "second ratio is (x+3)/(y+5) = 7/5.\r<BR>\n" );
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document.write( "solve for x in the first ratio to get x = 5y/3.\r<BR>\n" );
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document.write( "solve for (x+5) in the second ratio to get (x+3) = 7*(y+5)/5.<BR>\n" );
document.write( "simplify to get (x+3) = (7y+35)/5<BR>\n" );
document.write( "multiply both sides of that equation by 5 to get 5x+15 = 7y+35<BR>\n" );
document.write( "subtract 15 from both sides of that equation to get 5x = 7y+20<BR>\n" );
document.write( "replace x with 5y/3 fom the first equation to get 5*5y/3 = 7y+20<BR>\n" );
document.write( "simplify to get 25y/3 = 7y+20<BR>\n" );
document.write( "multiply both sides by 3 to get 25y = 21y+60<BR>\n" );
document.write( "subtract 21y from both sides to get 4y=60<BR>\n" );
document.write( "solve for y to get y = 60/4 = 15\r<BR>\n" );
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document.write( "the original ratio is x/y = 5/3<BR>\n" );
document.write( "when y = 15, the ratio becomes x/15 = 5/3<BR>\n" );
document.write( "solve for x to get x = 5*15/3 = 5*5 = 25\r<BR>\n" );
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document.write( "you have x = 25 and y = 3<BR>\n" );
document.write( "x is the number of girls.<BR>\n" );
document.write( "y is the number of boys.\r<BR>\n" );
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document.write( "the original ratio is 25/15 = 5/3.<BR>\n" );
document.write( "the revised ratio is 28/20 = 14/10 = 7/5.\r<BR>\n" );
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document.write( "both ratios are good, confirming the solution is correct.\r<BR>\n" );
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document.write( "the solution is there were 25 girls in the club originally.\r<BR>\n" );
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document.write( "i did a graphical solution and came up with the same answer.<BR>\n" );
document.write( "this is what it looks like.\r<BR>\n" );
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