document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1151779>Question 1151779</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a survey of 100 student the number of student studying various language where find to be: Arabic-28, french-30, yoruba-42, Arabic and yoruba-10, Arabic and french-8, french and yoruba-5, all the three language-3<BR>\n" );
document.write( "(1). How many student where studying no language<BR>\n" );
document.write( "(2). How many student had yoruba as their only language<BR>\n" );
document.write( "(3). How many student study french if and only if study yoruba </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #773626 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=773626\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i think it's going to work like this.<BR>\n" );
document.write( "you want to break each category up into different subgroups.<BR>\n" );
document.write( "start with the students that are leaning all 3.<BR>\n" );
document.write( "that's an only category, since it includes only students that are taking all 3.<BR>\n" );
document.write( "then work up to the category of pairs of courses.<BR>\n" );
document.write( "to make them pairs of courses only, you have to subtract the students who are taking all 3.\r<BR>\n" );
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document.write( "there are 10 students who are taking arabic and yoruba.  <BR>\n" );
document.write( "included is the students that are taking all 3.<BR>\n" );
document.write( "subtract 3 from this category and you have 7 students who are taking arabic and yoruba only.\r<BR>\n" );
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document.write( "there are 8 students who are taking arabic and french.<BR>\n" );
document.write( "included is the students that are taking all 3.<BR>\n" );
document.write( "subtract 3 from this category and you have 5 students who are taking arabic and french only.\r<BR>\n" );
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document.write( "there are 5 students who are taking french and yoruba.<BR>\n" );
document.write( "included is the students that are taking all 3.<BR>\n" );
document.write( "subtract 3 from this category and  you have 2 students who are taking french and yoruba only.\r<BR>\n" );
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document.write( "what you have now is:<BR>\n" );
document.write( "28 taking arabic<BR>\n" );
document.write( "30 taking french<BR>\n" );
document.write( "42 taking yoruba<BR>\n" );
document.write( "3 taking all 3 only.<BR>\n" );
document.write( "7 taking arabic and yoruba only.<BR>\n" );
document.write( "5 taking arabic and french only.<BR>\n" );
document.write( "2 taking french and yoruba only.\r<BR>\n" );
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document.write( "from the 28 who are taking arabic, you have to subtract 3 taking all 3 only and 7 taking arabic and yoruba only and 5 taking arabic and french only.<BR>\n" );
document.write( "this leave you with 28 - 3 - 7 - 5 = 13 who are taking arabic only.\r<BR>\n" );
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document.write( "from the 30 who are taking french, you have to subtract 3 taking all 3 only and 5 taking arabic and french only and 2 taking french and yoruba only.<BR>\n" );
document.write( "this leaves you with 30 - 3 - 5 - 2 = 20 who are taking french only.\r<BR>\n" );
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document.write( "from the 42 who are taking yoruba, you have to subtract 3 taking all 3 only and <BR>\n" );
document.write( "7 taking arabic and yoruba only and 2 taking french and yoruba only.<BR>\n" );
document.write( "this leave you with 42 - 3 - 7 - 2 = 30 taking yoruba only.\r<BR>\n" );
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document.write( "what you have now are:\r<BR>\n" );
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document.write( "only arabic = 13<BR>\n" );
document.write( "only french = 20<BR>\n" );
document.write( "only yoruba = 30<BR>\n" );
document.write( "only arabic and french = 5<BR>\n" );
document.write( "only arabic and yoruba = 7<BR>\n" );
document.write( "only french and yoruba = 2<BR>\n" );
document.write( "only arabic and french and yoruba = 3\r<BR>\n" );
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document.write( "this adds up to 80 students which means 20 students aren't studying any language at all since there are 100 students total.\r<BR>\n" );
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document.write( "you can work your way back up to the original figures by adding back the sub categories into their respective categories.\r<BR>\n" );
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document.write( "for example:<BR>\n" );
document.write( "13 students took arabic only.<BR>\n" );
document.write( "add 5 to include the students who took arabic and french only.<BR>\n" );
document.write( "add 7 to include the students who took arabic and yoruba only.<BR>\n" );
document.write( "add 3 to include the students who took all 3.<BR>\n" );
document.write( "you get a total of 13 + 5 + 7 + 3 = 28 students who took arabic.<BR>\n" );
document.write( "5 took arabic and french only.<BR>\n" );
document.write( "add 3 to include the students who took all 3.<BR>\n" );
document.write( "you get a total of 5 + 3 = 8 students who took arabic and french.\r<BR>\n" );
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document.write( "a generalized formula from the original numbers would be.\r<BR>\n" );
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document.write( "number who took arabic minus number who took pairs of courses that include arabic plus number who took all 3 = number who took arabic only.<BR>\n" );
document.write( "this would be 28 - 8 - 10 + 3 = 13\r<BR>\n" );
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document.write( "number who took french minus number who took pairs of courses that include french plus number who took all 3 = number who took french only.<BR>\n" );
document.write( "thi would be 30 - 8 - 5 + 3 = 20\r<BR>\n" );
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document.write( "number who took yoruba minus number who took pairs of courses that include yoruba plus number who took all 3 = number who took yoruba only.<BR>\n" );
document.write( "this would be 42 - 10 - 5 + 3 = 30.\r<BR>\n" );
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document.write( "working your way down, you would then subtract number who took all 3 from number who took pairs of courses.\r<BR>\n" );
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document.write( "for example, number who took arabic and french minus number who took all 3 = 7.\r<BR>\n" );
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document.write( "same idea for he others.\r<BR>\n" );
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document.write( "i made a chart which summarizes what was said above.<BR>\n" );
document.write( "what it looks like is shown below.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/012901.jpg\" alt = \"$$$\" >\r<BR>\n" );
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document.write( "in any case, you solution should be:<BR>\n" );
document.write( "(1). How many student where studying no language<BR>\n" );
document.write( "20 students were studying no language.\r<BR>\n" );
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document.write( "(2). How many student had yoruba as their only language<BR>\n" );
document.write( "30 students has yoruba as their only language.\r<BR>\n" );
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document.write( "(3). How many student study french if and only if study yoruba<BR>\n" );
document.write( "not sure how to interpret this one.<BR>\n" );
document.write( "i think this would be the students who study french and yoruba only.<BR>\n" );
document.write( "i believe this number is equal to 2.<BR>\n" );
document.write( "i don't think this would include the students who studied all 3 since that would include the students who studied arabic as well.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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