document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=246070>Question 246070</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Of 100 travelers, 10 understand neither English nor Russian. 75 know English, and 83 know Russian. How many travelers know both English and Russian? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #179720 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=179720\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 100 travelers total.\r<BR>\n" );
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document.write( "your categories are:\r<BR>\n" );
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document.write( "a = number travelers who know english.<BR>\n" );
document.write( "b = number of travelers who know russian.<BR>\n" );
document.write( "c = number of travelers who do not know english and do not know russian.<BR>\n" );
document.write( "d = number of travelers who know both english and russian.\r<BR>\n" );
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document.write( "a + b + c - d = 100\r<BR>\n" );
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document.write( "a = 75<BR>\n" );
document.write( "b = 83<BR>\n" );
document.write( "c = 10<BR>\n" );
document.write( "d = ?????\r<BR>\n" );
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document.write( "75 + 83 + 10 - d = 100<BR>\n" );
document.write( "168 - d = 100<BR>\n" );
document.write( "d = 68\r<BR>\n" );
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document.write( "You have 68 people who know english and russian.\r<BR>\n" );
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document.write( "here's how it works\r<BR>\n" );
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document.write( "you have 75 people who know english.\r<BR>\n" );
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document.write( "this includes 68 people who know english and russian.\r<BR>\n" );
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document.write( "you have 83 people who know russian.\r<BR>\n" );
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document.write( "this includes 68 people who know english and russian.\r<BR>\n" );
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document.write( "the people who know english and russian are being counted twice.   Once in the english group and once in the russian group.\r<BR>\n" );
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document.write( "You remove the double counting by subtracting them one time.\r<BR>\n" );
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document.write( "75 + 83 + 10 - 68 = 100\r<BR>\n" );
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document.write( "Another way to accomplish this would be to create new categories as follows:\r<BR>\n" );
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document.write( "f = speak english only<BR>\n" );
document.write( "g = speak russian only<BR>\n" );
document.write( "h = not speak (english and russian)<BR>\n" );
document.write( "i = speak both english and russian\r<BR>\n" );
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document.write( "your numbers would be:\r<BR>\n" );
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document.write( "7 + 15 + 10 + 68 = 100\r<BR>\n" );
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document.write( " </SPAN>\n" );
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