document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1001702>Question 1001702</A>: <I><SPAN STYLE=\"word-break: break-all;\"> in a recent survey of 400 students in a school, 100 were listed as smokers and 150 as gum chewers. 75 were listed as smokers and gum chewers. find how many students are neither smokers nor gum chewers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #618788 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=618788\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 100 smokers<BR>\n" );
document.write( "150 gum chewers<BR>\n" );
document.write( "75 smokers and gum chewers.<BR>\n" );
document.write( "total is 400.\r<BR>\n" );
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document.write( "formula says A or B = A + B - A and B.\r<BR>\n" );
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document.write( "A is the smokers<BR>\n" );
document.write( "B is the gum chewers<BR>\n" );
document.write( "A and B is the ones who do both.<BR>\n" );
document.write( "A or B is the ones who do one or the other or both.\r<BR>\n" );
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document.write( "A = 100<BR>\n" );
document.write( "B = 150<BR>\n" );
document.write( "A and B = 75\r<BR>\n" );
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document.write( "by the formula, you get:\r<BR>\n" );
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document.write( "A or B = 100 + 150 - 75 = 250 - 75 = 175.\r<BR>\n" );
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document.write( "since there are 400 total, the ones who do neither are 400 - 175 = 225.\r<BR>\n" );
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document.write( "another way of looking at it is:\r<BR>\n" );
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document.write( "100 smokers, 75 of which chew gum as well.<BR>\n" );
document.write( "break that up into:<BR>\n" );
document.write( "25 smokers only.<BR>\n" );
document.write( "75 smokers who chew gum also.\r<BR>\n" );
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document.write( "150 gum chewers, 75 of which smoke as well.<BR>\n" );
document.write( "break that up into9:<BR>\n" );
document.write( "75 who chew gum only.<BR>\n" );
document.write( "75 who chew gum and smoke also.\r<BR>\n" );
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document.write( "you now have 3 categories.\r<BR>\n" );
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document.write( "25 smoke only.<BR>\n" );
document.write( "75 chew gum only.<BR>\n" );
document.write( "75 chew gum and smoke.\r<BR>\n" );
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document.write( "those categories are now clean, i.e. they do not include anybody who is also in another category.\r<BR>\n" );
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document.write( "add them up and you get 175.\r<BR>\n" );
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document.write( "400 - 175 = 225 which are the ones who do neither.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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