document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=126497>Question 126497</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please show me how to solve this problem ( it was a homework problem (1 complete problem) and I didn't know where to start).  thanks!\r<BR>\n" );
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document.write( "200 Students\r<BR>\n" );
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document.write( "70 Students take English class<BR>\n" );
document.write( "54 Students take Math class<BR>\n" );
document.write( "45 Students take Social Studies<BR>\n" );
document.write( "28 Students take English and Math<BR>\n" );
document.write( "19 Students take English and Scial Studies<BR>\n" );
document.write( "15 Students take Math and Scial Studies<BR>\n" );
document.write( "10 Students take English, Math and Social Studies\r<BR>\n" );
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document.write( "1.) How many students take English<BR>\n" );
document.write( "2.) How many Students take math only<BR>\n" );
document.write( "3.) How many Students take English, social studies but not math<BR>\n" );
document.write( "4.) How many students take math and social studies but not English class<BR>\n" );
document.write( "5.) How many do not take any class. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #92700 by </B><A HREF=/tutors/aboutme.mpl?userid=marcsam823><B>marcsam823(57)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=marcsam823><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=92700\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since this problem contains several elements that are more easily tracked with a picture, I find the easiest way to solve it is with a Venn Diagram.  Venn Diagrams are basically a series of overlapping circles that allow you to see all at once how your data relates. I can't draw Venn diagrams on this site, but if you'd like to learn more about them, go this site:\r<BR>\n" );
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document.write( "http://en.wikipedia.org/wiki/Venn_diagram and click the Examples hyperlink.\r<BR>\n" );
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document.write( "Question 1)<BR>\n" );
document.write( "We are given that a total of 70 students take English class. These students can be divided into 4 groups:<BR>\n" );
document.write( "a =  Students who take English, Math and Social Studies<BR>\n" );
document.write( "b =  Students who take English and Social Studies only<BR>\n" );
document.write( "c =  Students who take English and Math only<BR>\n" );
document.write( "d =  Students who take English only<BR>\n" );
document.write( "a + b + c + d = 70  = Total students taking English \r<BR>\n" );
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document.write( "1. The problem gives us <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+10 ALIGN=MIDDLE  ALT=\"a+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" > students who take all 3 classes. This is a good start, because it will help us solve for b  and c \r<BR>\n" );
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document.write( "2. Solve for b:<BR>\n" );
document.write( "The problem also tells us that 19 students take English and Social Studies.  This can be a little confusing because this 19 also includes the 10 that are taking Math as well.<BR>\n" );
document.write( "Therefore: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19+-+10+=+b+=+9 ALIGN=MIDDLE  ALT=\"19+-+10+=+b+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >  students taking English and Social Studies ONLY.\r<BR>\n" );
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document.write( "3. Solve for c:<BR>\n" );
document.write( "Similarly, we are given that 28 students are taking English and Math Therefore: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28+-+10+=+c+=+18 ALIGN=MIDDLE  ALT=\"28+-+10+=+c+=+18\"   DISABLED_style= \"max-width:90%; height:auto;\" > students taking English and Math ONLY.\r<BR>\n" );
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document.write( "4. Now we can solve for d, students who take English only: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2B+b+%2B+c+%2B+d+=+70 ALIGN=MIDDLE  ALT=\"a+%2B+b+%2B+c+%2B+d+=+70\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10+%2B+9+%2B+18+%2B+d+=+70 ALIGN=MIDDLE  ALT=\"10+%2B+9+%2B+18+%2B+d+=+70\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=37+%2B+d+=+70 ALIGN=MIDDLE  ALT=\"37+%2B+d+=+70\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+33 ALIGN=MIDDLE  ALT=\"d+=+33\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "33 students take English only.\r<BR>\n" );
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document.write( "Question 2)<BR>\n" );
document.write( "We are given that a total of 54 students take math class. These students can be divided into 4 groups:<BR>\n" );
document.write( "a =  Students who take Math, English and Social Studies<BR>\n" );
document.write( "c =  Students who take Math and English only<BR>\n" );
document.write( "e =  Students who take Math and Social Studies only<BR>\n" );
document.write( "f =  Students who take Math only\r<BR>\n" );
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document.write( "a + c + e + f = 54 = Total students taking Math\r<BR>\n" );
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document.write( "Notice from question 1) we already have values for a and c so let's substitute:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10+%2B+18+%2B+e+%2B+f+=+54 ALIGN=MIDDLE  ALT=\"10+%2B+18+%2B+e+%2B+f+=+54\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "so we don't have to do as much work for this part of the problem.\r<BR>\n" );
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document.write( "1. Solve for e:<BR>\n" );
document.write( "The problem also tells us that 15 students take Math and Social Studies.  This can be a little confusing because this 15 also includes the 10 that are taking English as well.<BR>\n" );
document.write( "Therefore: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15+-+10+=+e+=+5 ALIGN=MIDDLE  ALT=\"15+-+10+=+e+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >  students taking Math and Social Studies ONLY.\r<BR>\n" );
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document.write( "2. Now we can solve for f, students who take Math only. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2B+c+%2B+e+%2B+f+=+54 ALIGN=MIDDLE  ALT=\"a+%2B+c+%2B+e+%2B+f+=+54\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10+%2B+18+%2B+5+%2B+f+=+54 ALIGN=MIDDLE  ALT=\"10+%2B+18+%2B+5+%2B+f+=+54\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=33+%2B+f+=+54 ALIGN=MIDDLE  ALT=\"33+%2B+f+=+54\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f+=+21 ALIGN=MIDDLE  ALT=\"f+=+21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "21 students take Math only.\r<BR>\n" );
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document.write( "Question 3)<BR>\n" );
document.write( "We've already done the work for this one! The total number of students who take English and Social Studies only is 9.  (Our b variable from question 1)\r<BR>\n" );
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document.write( "Question 4)<BR>\n" );
document.write( "We've done this one too! The total number of students who take math and social studies only is 5 (Our e variable from Question 2)\r<BR>\n" );
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document.write( "Question 5)<BR>\n" );
document.write( "In order to find how many students are not taking classes we need to find the total number students who ARE.<BR>\n" );
document.write( "We have all the elements we need except for one: <BR>\n" );
document.write( "a = students take all three classes = 10 <BR>\n" );
document.write( "b = students taking English and Social Studies  DISABLED_event_only=  9<BR>\n" );
document.write( "c = students taking English and Math  DISABLED_event_only=  18<BR>\n" );
document.write( "d = students taking English  DISABLED_event_only=  33<BR>\n" );
document.write( "e = students taking Math and Social Studies  DISABLED_event_only=  5<BR>\n" );
document.write( "f = students taking Math  DISABLED_event_only=  21<BR>\n" );
document.write( "g = students taking Social Studies  DISABLED_event_only=  ???\r<BR>\n" );
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document.write( "1. We need to find a value for g:<BR>\n" );
document.write( "We are told that a total of 45 are taking Social studies. This includes:<BR>\n" );
document.write( "a = 10 = students taking all three classes<BR>\n" );
document.write( "b = 9 = students taking Social Studies and English only <BR>\n" );
document.write( "e = 5 = students taking Social studies and Math only <BR>\n" );
document.write( "g = ?\r<BR>\n" );
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document.write( "2. Solve for g:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2B+b+%2B+e+%2B+g+=+45 ALIGN=MIDDLE  ALT=\"a+%2B+b+%2B+e+%2B+g+=+45\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10+%2B+9+%2B+5+%2B+g+=+45 ALIGN=MIDDLE  ALT=\"10+%2B+9+%2B+5+%2B+g+=+45\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24+%2B+g+=+45 ALIGN=MIDDLE  ALT=\"24+%2B+g+=+45\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g+=+21 ALIGN=MIDDLE  ALT=\"g+=+21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "21 students take Social Studies only\r<BR>\n" );
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document.write( "3. Subtract from total student body of 200: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200+-+%28a+%2B+b+%2B+c+%2B+d+%2B+e+%2B+f+%2B+g%29 ALIGN=MIDDLE  ALT=\"200+-+%28a+%2B+b+%2B+c+%2B+d+%2B+e+%2B+f+%2B+g%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = Students not taking a class<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200+-+%2810+%2B+9+%2B+18+%2B+33+%2B+5+%2B+21+%2B+21%29 ALIGN=MIDDLE  ALT=\"200+-+%2810+%2B+9+%2B+18+%2B+33+%2B+5+%2B+21+%2B+21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200+-+117+=+83 ALIGN=MIDDLE  ALT=\"200+-+117+=+83\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "83 students do not take English, Math or Social Studies.    \r<BR>\n" );
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document.write( "Just a Reminder:<BR>\n" );
document.write( " A Venn diagram would have made this problem a lot easier.  You would simply draw 3 overlapping circles. Label one \"Math\", one \"English\" and one \"Social Studies\". Each section created by an overlap is equal to one of the letters we used (there should be 7, a through g). To keep track of the total number of groups of students simply count the number of sections and label each with a letter. <BR>\n" );
document.write( "a) Sections where no overlap occurs are for those students enrolled in one class only (there will be three sections like this)<BR>\n" );
document.write( "b) Sections where two of the circles overlap are for those students who are enrolled in two classes (there will be three of these)<BR>\n" );
document.write( "c) There will be one section where all three circles overlap for the 10 students taking all three classes.<BR>\n" );
document.write( "In math, it is always easier to have a picture of your problem handy!\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );