document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=34448>Question 34448</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the Junior Class the Followin statistics are true...<BR>\n" );
document.write( "*116 students take algebra II<BR>\n" );
document.write( "*99 students take Chemistry<BR>\n" );
document.write( "*49 take Spanish<BR>\n" );
document.write( "*15 students that take algebra II also take Chemistry<BR>\n" );
document.write( "*20 students that take algebra II also take Spanish<BR>\n" );
document.write( "*22 students that take Chemistry also take Spanish<BR>\n" );
document.write( "*12 students take Chemistry algebra II and Spanish<BR>\n" );
document.write( "*31 students take none of th three classes\r<BR>\n" );
document.write( "\n" );
document.write( "How many students are in the class?<BR>\n" );
document.write( "I know the answer is 250... i solved it using a venn diagram and the teacher said it was right... but he said that there is a formulaic way to solve it and is giving MAJOR bonus points if i figure it out... so PLEASE i nned it solved out mathatmatically (meaning a formula) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #20696 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=20696\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> SEE MY WORKING BELOW...<BR>\n" );
document.write( "I AM USING * SYMBOL FOR INTERSECTION...X*Y MEANS X INTERSECTION Y.<BR>\n" );
document.write( " AND # SYMBOL FOR UNION .....X#Y MEANS X UNION Y.<BR>\n" );
document.write( "AND | MEANS COMPLEMENT OR NEGATION.....X| MEANS NOT X.<BR>\n" );
document.write( "In the Junior Class the Followin statistics are true...<BR>\n" );
document.write( "*116 students take algebra II...=A SAY<BR>\n" );
document.write( "*99 students take Chemistry.....=C SAY<BR>\n" );
document.write( "*49 take Spanish................=S SAY<BR>\n" );
document.write( "*15 students that take algebra II also take Chemistry...= A AND C = A*C<BR>\n" );
document.write( "*20 students that take algebra II also take Spanish.....= A AND S = A*S<BR>\n" );
document.write( "*22 students that take Chemistry also take Spanish......= C AND S = C*S<BR>\n" );
document.write( "*12 students take Chemistry algebra II and Spanish......= C AND A AND S = C*A*S<BR>\n" );
document.write( "*31 students take none of th three classes..............= NEITHER C NOR A NOR S = (C|)#(A|)#(S|)<BR>\n" );
document.write( "How many students are in the class?<BR>\n" );
document.write( "I know the answer is 250... i solved it using a venn diagram and the teacher said it was right...<BR>\n" );
document.write( "NOW LOOK AT YOUR VENN DIAGRAM AND ANALYSE....YOU WILL FIND...<BR>\n" );
document.write( "A INCLUDES FOUR DISJOINT OR SEPERATE PARTS.. A*C ONLY,A*S ONLY, A ONLY AND FINALLY  A AND C AND S <BR>\n" );
document.write( "SIMILARLY<BR>\n" );
document.write( "C INCLUDES FOUR DISJOINT OR SEPERATE PARTS.. C*A ONLY,C*S ONLY,C ONLY AND FINALLY C AND A AND S<BR>\n" );
document.write( "SIMILARLY<BR>\n" );
document.write( "S INCLUDES FOUR DISJOINT OR SEPERATE PARTS.. S*A ONLY,S*C ONLY,S ONLY AND<BR>\n" );
document.write( "FINALLY S AND A AND C.<BR>\n" );
document.write( "HENCE IF WE TOTAL A,C AND S WE GET A#C#S=TOTAL NUMBER OF STUDENTS TAKING ANY ONE OR MORE OF THESE 3 TOPICS BUT INCUDING THE DUPLICATED COUNTS OF THOSE TAKING MORE  THAN ONE TOPIC...FURTHER WE FIND WITHIN THOSE ARE THERE TAKING ONLY ONE TOPIC,ONLY 2 TOPICS AND ALL 3 TOPICS..THAT IS MATHEMATICALLY SPEAKING <BR>\n" );
document.write( "A INCUDES A*C AND A*C INCLUDES A*C*S...SIMILAR LOGIC HOLDS FOR ALL OTHER PARAMETERS...NOW WITH THE HELP OF VENN DIAGRAM ,WE CAN REMOVE THIS DUPLICATION..METHODICLLY AS FOLLOWS<BR>\n" );
document.write( "TOTAL NUMBER OF STUDENTS TAKING ANY ONE OF THE 3 TOPICS(T) <BR>\n" );
document.write( "T=(A#C#S)-{A*C+A*S+C*S-(A*C*S)}=A#C#S-A*C-A*S-C*S+A*C*S<BR>\n" );
document.write( "TO GET THE TOTAL NUMBER OF STUDENTS IN THE CLASS (G.T)WE SHOULD ADD TO THE ABOVE THE NUMBER OF STUDENTS TAKING NONE OF THE ABOVE 3 TOPICS..THAT IS <BR>\n" );
document.write( "G.T=A#C#S-A*C-A*S-C*S+A*C*S+A|#C|#S|<BR>\n" );
document.write( "=116+99+49-15-20-22+12+31=250<BR>\n" );
document.write( "THAT IS YOUR MATHEMATICAL FORMULA,,<BR>\n" );
document.write( "HOPE YOU UNDERSTOOD AND YOU WILL GET YOUR BONUS SCORE...DONT FORGET TO REPLACE THE ABOVE SYMBOLS FOR INTERSECTION(*),UNION(#) AND NEGATION (|)WITH PROPER MATHS<BR>\n" );
document.write( "SYMBOLS\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " but he said that there is a formulaic way to solve it and is giving MAJOR bonus points if i figure it out... so PLEASE i nned it solved out mathatmatically (meaning a formula) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );