document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1183899>Question 1183899</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A group of 35 students performed in a school program. out of the 35,18 sang,19,danced, and 7 sang and danced Venn diagram​. thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #814391 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=814391\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you are stating that.....\r<BR>\n" );
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document.write( "there are a total of 35 students.\r<BR>\n" );
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document.write( "18 sang<BR>\n" );
document.write( "19 danced<BR>\n" );
document.write( "7 sand and danced.\r<BR>\n" );
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document.write( "your numbers don't add up.\r<BR>\n" );
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document.write( "first of all.\r<BR>\n" );
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document.write( "if there are 35 students total,  and 18 of them sang and 19 of them danced, that gets you a total of 37 students, assuming that none of hem both sang and danced.\r<BR>\n" );
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document.write( "in order for there to be 35 students total, 2 of them must have sang and danced.\r<BR>\n" );
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document.write( "that would give you 16 who sang only and 17 who danced only and 2 who sang and danced for a total of 35 students.\r<BR>\n" );
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document.write( "if you had 18 students who sang and 19 students who danced and 7 who sang and danced, and the 7 who sang and danced were included in the number of those who sang and those who danced, then you would get:\r<BR>\n" );
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document.write( "11 sand only and 12 danced only and 7 sang and danced.\r<BR>\n" );
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document.write( "that would give you a total of 30 students.\r<BR>\n" );
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document.write( "if you had 18 students who sang and 19 students who danced and 7 who sand and danced, and the 7 who sand and danced were not included in the number of those who sang and those who danced, then you would get:\r<BR>\n" );
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document.write( "18 sand only and 19 danced only and 7 sang and danced.\r<BR>\n" );
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document.write( "that would give you a total of 44 students.\r<BR>\n" );
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document.write( "bottom line:\r<BR>\n" );
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document.write( "you have a prblem with your numbers.\r<BR>\n" );
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document.write( "it could not be 35 students.<BR>\n" );
document.write( "it would only be 30 or 44.\r<BR>\n" );
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document.write( "here are my two venn diagrams that capture what i think is the case.\r<BR>\n" );
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document.write( "the first venn diagram is assuming that the 7 who sang and danced were included in the number of those who sang and those who danced.\r<BR>\n" );
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document.write( "the second venn diagram is assuming that the 7 who sang and danced were not included in the number of those who sang and those who danced.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/082602.jpg\" >\r<BR>\n" );
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document.write( "neither of these two options will get you a total of 35 students.\r<BR>\n" );
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document.write( "you need to go back and check again what they are asking you to do.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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