document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203641>Question 1203641</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi<BR>\n" );
document.write( "In a fish tank there were 35 more guppies than goldfish. When more guppies and goldfish were added the number of guppies increased by 1/6 and the number of goldfish by 3/5 . Then the total number of fish in the tank was 193. How many guppies were there in the end. <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 #839367 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=839367\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> g = number of guppies<BR>\n" );
document.write( "f = number of goldfish<BR>\n" );
document.write( "g = f + 35\r<BR>\n" );
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document.write( "g + 1/6 * g + f + 3/5 * f = 193<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "7/6 * g + 8/5 * f = 193\r<BR>\n" );
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document.write( "you are given that g = f + 35<BR>\n" );
document.write( "replace g in the equation of 7/6 * g + 8/5 * f = 193 with f + 35 to get:<BR>\n" );
document.write( "7/6 * (f + 35) + 8/5 * f = 193<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "7/6 * f + 7/6 * 35 + 8/5 * f = 193\r<BR>\n" );
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document.write( "multiply both sides of the equation by 30 to get:<BR>\n" );
document.write( "35 * f + 35 * 35 + 48 * f = 193 * 30<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "35 * f + 1225 + 48 * f = 5790\r<BR>\n" );
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document.write( "combine like terms to get:<BR>\n" );
document.write( "83 * f + 1225 = 5790<BR>\n" );
document.write( "subtract 1225 from both sides of the equation to get:<BR>\n" );
document.write( "83 * f = 4565<BR>\n" );
document.write( "solve for f to get:<BR>\n" );
document.write( "f = 55\r<BR>\n" );
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document.write( "since g = f + 35, then you get:<BR>\n" );
document.write( "f = 55<BR>\n" );
document.write( "g = 90\r<BR>\n" );
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document.write( "confirm by replacing g and f in the original equations to get:\r<BR>\n" );
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document.write( "g = f + 35 becomes 90 = 55 + 35 which becomes 90 = 90.<BR>\n" );
document.write( "this confirmns that g = f + 35 is true.\r<BR>\n" );
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document.write( "g + 1/6 * g + f + 3/5 * f = 193 becomes:<BR>\n" );
document.write( "90 + 1/6 * 90 + 55 + 3/5 * 55 = 193 which becomes:<BR>\n" );
document.write( "105 + 88 = 193 which becomes 193 = 193.<BR>\n" );
document.write( "this confirms that g + 1/6 * g + f + 3/5 * f is true.\r<BR>\n" );
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document.write( "your solution is that there were 105 guppies in the end.<BR>\n" );
document.write( "that would be 90 guppies to start plus 1/6 * 90 = 15 guppies for a total of 105 guppies in the end.\r<BR>\n" );
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