document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1151451>Question 1151451</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There were two competitions in a puzzle tournament. The Sudoku competition<BR>\n" );
document.write( "had twice as many participants as the Crossword competition. If 225 people<BR>\n" );
document.write( "competed overall, and 60 of them participated in both competitions, how many<BR>\n" );
document.write( "people participated in the Sudoku competition?<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 #773191 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=773191\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = number of sudoku competition players.<BR>\n" );
document.write( "y = number of crossword competition players.<BR>\n" );
document.write( "60 = number of participants in both competitions.\r<BR>\n" );
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document.write( "since the number of participants in both is included in the total of each, you have:\r<BR>\n" );
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document.write( "x + y - 60 = 225<BR>\n" );
document.write( "x + y = 285<BR>\n" );
document.write( "y = 2x<BR>\n" );
document.write( "3x = 285<BR>\n" );
document.write( "x = 95<BR>\n" );
document.write( "y = 190\r<BR>\n" );
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document.write( "you have 95 people who competed in the sudoku competition and 190 who competed in the crossword competition.\r<BR>\n" );
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document.write( "of the 95 who competed in the sudoku competition, 60 also competed in the crossword competition.\r<BR>\n" );
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document.write( "therefore, you have:<BR>\n" );
document.write( "35 who competed only in the sudoku competition.<BR>\n" );
document.write( "130 who competed only in the crossword competition.<BR>\n" );
document.write( "60 who competed in both.\r<BR>\n" );
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document.write( "total who competed in both competitions is 35 + 130 + 60 = 225\r<BR>\n" );
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document.write( "the question is how many competed in the sudoku competition.\r<BR>\n" );
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document.write( "that would be 35 + 60 = 95.\r<BR>\n" );
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document.write( "the basic assumption is that the number who competed in both are counted in the number who competed in each.\r<BR>\n" );
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document.write( "that means they are being double counted and so one of them needs to be subtracted out.\r<BR>\n" );
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document.write( "that's why you get x + y - 60 = 225.\r<BR>\n" );
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document.write( "that becomes your basic equation that you use to solve for x and y, taking nto account that y = 2x.\r<BR>\n" );
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