document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209540>Question 1209540</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A total of 90 students selected from some schools for Science and Math quiz were asked to indicate the meal they prefer: Banku, Rice and Fufu. The results showed that 63 liked Banku(B), 55 liked Rice(R) and 50 Fufu(F). 13 liked Banku only, 8 Rice only, 5 Fufu only and 22 liked all three meals. <BR>\n" );
document.write( "(a) Draw a Venn diagram to illustrate information. <BR>\n" );
document.write( "(b) Find the number of students who liked:<BR>\n" );
document.write( "(i) Banku and Rice<BR>\n" );
document.write( "(ii) only two of the meals<BR>\n" );
document.write( "(iii) none of the three meals<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849388 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=849388\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Based on this info \"<font color=blue>13 liked Banku only, 8 Rice only, 5 Fufu only and 22 liked all three meals</font>\" we would have this Venn Diagram so far.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C400%2C-5%2C5%2C-5%2C5%2C%0D%0Aline%28-4%2C4%2C4%2C4%29%2C%0D%0Aline%284%2C4%2C4%2C-4%29%2C%0D%0Aline%284%2C-4%2C-4%2C-4%29%2C%0D%0Aline%28-4%2C-4%2C-4%2C4%29%2C%0D%0A%0D%0Acircle%28-1%2C1%2C2%29%2Ccircle%281%2C1%2C2%29%2Ccircle%280%2C-0.7321%2C2%29%2C%0D%0A%0D%0Alocate%28-2.8-0.5%2C2.8%2CBanku%29%2C%0D%0Alocate%282.6%2C2.8%2CRice%29%2C%0D%0Alocate%281%2C-2.6%2CFufu%29%2C%0D%0Alocate%28-2%2C1.8%2C13%29%2C%0D%0Alocate%280%2C1.8%2Ca%29%2C%0D%0Alocate%282%2C1.8%2C8%29%2C%0D%0Alocate%28-1.5%2C0%2Cb%29%2C%0D%0Alocate%280%2C0.4%2C22%29%2C%0D%0Alocate%281.2%2C0%2Cc%29%2C%0D%0Alocate%280%2C-1.5%2C5%29%2C%0D%0Alocate%283%2C-1.5%2Cd%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Because \"<font color=blue>The results showed that 63 liked Banku(B), 55 liked Rice(R) and 50 Fufu(F)</font>\", we can form this system of equations<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%2813%2Ba%2Bb%2B22+=+63%2Ca%2B8%2B22%2Bc=55%2Cb%2B22%2Bc%2B5=50%29 ALIGN=MIDDLE  ALT=\"system%2813%2Ba%2Bb%2B22+=+63%2Ca%2B8%2B22%2Bc=55%2Cb%2B22%2Bc%2B5=50%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Each equation is the result of adding the numbers in the circles shown.<BR>\n" );
document.write( "Solving this system leads to a = 15, b = 13, c = 10. <BR>\n" );
document.write( "I'll let the student handle the scratch work.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If we plug in those a,b,c values then we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C400%2C-5%2C5%2C-5%2C5%2C%0D%0Aline%28-4%2C4%2C4%2C4%29%2C%0D%0Aline%284%2C4%2C4%2C-4%29%2C%0D%0Aline%284%2C-4%2C-4%2C-4%29%2C%0D%0Aline%28-4%2C-4%2C-4%2C4%29%2C%0D%0A%0D%0Acircle%28-1%2C1%2C2%29%2Ccircle%281%2C1%2C2%29%2Ccircle%280%2C-0.7321%2C2%29%2C%0D%0A%0D%0Alocate%28-2.8-0.5%2C2.8%2CBanku%29%2C%0D%0Alocate%282.6%2C2.8%2CRice%29%2C%0D%0Alocate%281%2C-2.6%2CFufu%29%2C%0D%0Alocate%28-2%2C1.8%2C13%29%2C%0D%0Alocate%280%2C1.8%2C15%29%2C%0D%0Alocate%282%2C1.8%2C8%29%2C%0D%0Alocate%28-1.5%2C0%2C13%29%2C%0D%0Alocate%280%2C0.4%2C22%29%2C%0D%0Alocate%281.2%2C0%2C10%29%2C%0D%0Alocate%280%2C-1.5%2C5%29%2C%0D%0Alocate%283%2C-1.5%2Cd%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Adding up all the values in the Venn Diagram should get us 90 total students.<BR>\n" );
document.write( "13+15+8+13+22+10+5+d = 90<BR>\n" );
document.write( "86+d = 90<BR>\n" );
document.write( "d = 90-86<BR>\n" );
document.write( "d = 4\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The completed Venn Diagram is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C400%2C-5%2C5%2C-5%2C5%2C%0D%0Aline%28-4%2C4%2C4%2C4%29%2C%0D%0Aline%284%2C4%2C4%2C-4%29%2C%0D%0Aline%284%2C-4%2C-4%2C-4%29%2C%0D%0Aline%28-4%2C-4%2C-4%2C4%29%2C%0D%0A%0D%0Acircle%28-1%2C1%2C2%29%2Ccircle%281%2C1%2C2%29%2Ccircle%280%2C-0.7321%2C2%29%2C%0D%0A%0D%0Alocate%28-2.8-0.5%2C2.8%2CBanku%29%2C%0D%0Alocate%282.6%2C2.8%2CRice%29%2C%0D%0Alocate%281%2C-2.6%2CFufu%29%2C%0D%0Alocate%28-2%2C1.8%2C13%29%2C%0D%0Alocate%280%2C1.8%2C15%29%2C%0D%0Alocate%282%2C1.8%2C8%29%2C%0D%0Alocate%28-1.5%2C0%2C13%29%2C%0D%0Alocate%280%2C0.4%2C22%29%2C%0D%0Alocate%281.2%2C0%2C10%29%2C%0D%0Alocate%280%2C-1.5%2C5%29%2C%0D%0Alocate%283%2C-1.5%2C4%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Part (a) is completed at this point. <BR>\n" );
document.write( "I'll let the student handle part (b).<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );