document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1182254>Question 1182254</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this: 90 principal accountants from selected shs <BR>\n" );
document.write( "attended a one week workshop at ajumako and the following shows their choice<BR>\n" );
document.write( "of meal they prefer at lunch. 63 like Banku with stew (B) 55 like fried rice<BR>\n" );
document.write( "with chicken (R) and 50 like fufu with mutton light soup. (F) 13 liked only<BR>\n" );
document.write( "Banku 8 liked only fried rice 5 like only fufu and 22 liked all three meals.<BR>\n" );
document.write( "Find the number of accountants who liked<BR>\n" );
document.write( "a. Banku and fried rice<BR>\n" );
document.write( "b. Only two of the meals<BR>\n" );
document.write( "c. None of the three meals. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #812305 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=812305\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The other tutor started the solution using 8 variables; that is fine, but I think unnecessarily complicated, since we are given the values of 4 of those variables.<br><BR>\n" );
document.write( "So I'm going to pirate his nice diagram and solve the problem using far fewer variables, leading to a much easier solution.<br><BR>\n" );
document.write( "His diagram....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-4%2C4%2C-5%2C4%2C%0D%0Arectangle%28-4%2C-3.5%2C4%2C4%29%2C%0D%0Acircle%280%2C-.5%2C2%29%2C%0D%0Alocate%28-2.3%2C2%2C%22s=%3F%22%29%2C%0D%0Alocate%28-3.5%2C-2%2C%22z=%3F%22%29%2C%0D%0Alocate%280%2C-2.7%2CF%29%2C%0D%0Alocate%28-.45%2C-1%2C%22y=%3F%22%29%2C%0D%0Alocate%28.6%2C.4%2C%22x=%3F%22%29%2C+%0D%0Acircle%28sqrt%282%29%2Csqrt%282%29%2C2%29%2C+%0D%0Alocate%28-3.5%2C2.5%2CB%29%2C%0D%0Acircle%28-sqrt%282%29%2Csqrt%282%29%2C2%29%2C%0D%0Alocate%283.5%2C2.5%2CR%29%2C%0D%0Alocate%28-1.5%2C.5%2C%22v=%3F%22%29%2C%0D%0Alocate%28-.4%2C2.3%2C%22t=%3F%22%29%2C%0D%0Alocate%281.8%2C2%2C%22u=%3F%22%29%2C%0D%0Alocate%28-.4%2C1.1%2C%22w=%3F%22%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "A revised diagram, using given numbers where possible....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-4%2C4%2C-5%2C4%2C%0D%0Arectangle%28-4%2C-3.5%2C4%2C4%29%2C%0D%0Acircle%280%2C-.5%2C2%29%2C%0D%0Alocate%28-2.3%2C2%2C13%29%2C%0D%0Alocate%280%2C-2.7%2C%22F=50%22%29%2C%0D%0Alocate%28-.45%2C-1%2C5%29%2C%0D%0Alocate%28.6%2C.4%2C%22b%22%29%2C+%0D%0Acircle%28sqrt%282%29%2Csqrt%282%29%2C2%29%2C+%0D%0Alocate%28-3.9%2C3%2C%22B=63%22%29%2C%0D%0Acircle%28-sqrt%282%29%2Csqrt%282%29%2C2%29%2C%0D%0Alocate%283%2C3%2C%22R=55%22%29%2C%0D%0Alocate%28-1.5%2C.5%2C%22c%22%29%2C%0D%0Alocate%28-.4%2C2.3%2C%22a%22%29%2C%0D%0Alocate%281.8%2C2%2C8%29%2C%0D%0Alocate%28-.4%2C1.1%2C22%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "With this diagram, I have only three variables, with the following three equations:<br><BR>\n" );
document.write( "B: a+c+22+13=63; a+c=28 [1]<BR>\n" );
document.write( "R: a+b+22+8=55; a+b=25 [2]<BR>\n" );
document.write( "F: b+c+22+5=50; b+c=23 [3]<br><BR>\n" );
document.write( "With these three equations, we can easily find a+b+c...<br><BR>\n" );
document.write( "Adding [1]+[2]+[3]...<br><BR>\n" );
document.write( "2(a+b+c)=76<BR>\n" );
document.write( "a+b+c=38 [4]<br><BR>\n" );
document.write( "... then it is easy to solve for a, b, and c, by comparing [4] with [1], [2], and [3]:<br><BR>\n" );
document.write( "a = 38-23=15<BR>\n" );
document.write( "b=38-28=10<BR>\n" );
document.write( "c=38-25=13<br><BR>\n" );
document.write( "Now the diagram is this:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-4%2C4%2C-5%2C4%2C%0D%0Arectangle%28-4%2C-3.5%2C4%2C4%29%2C%0D%0Acircle%280%2C-.5%2C2%29%2C%0D%0Alocate%28-2.3%2C2%2C13%29%2C%0D%0Alocate%280%2C-2.7%2C%22F=50%22%29%2C%0D%0Alocate%28-.45%2C-1%2C5%29%2C%0D%0Alocate%28.6%2C.4%2C10%29%2C+%0D%0Acircle%28sqrt%282%29%2Csqrt%282%29%2C2%29%2C+%0D%0Alocate%28-3.9%2C3%2C%22B=63%22%29%2C%0D%0Acircle%28-sqrt%282%29%2Csqrt%282%29%2C2%29%2C%0D%0Alocate%283%2C3%2C%22R=55%22%29%2C%0D%0Alocate%28-1.5%2C.5%2C13%29%2C%0D%0Alocate%28-.4%2C2.3%2C15%29%2C%0D%0Alocate%281.8%2C2%2C8%29%2C%0D%0Alocate%28-.4%2C1.1%2C22%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Now we can answer the questions....<br><BR>\n" );
document.write( "a. How many like Banku and fried rice<BR>\n" );
document.write( "22+a = 22+15 = 37<br><BR>\n" );
document.write( "b. How many like only two of the meals<BR>\n" );
document.write( "a+b+c = 15+10+13 = 38<br><BR>\n" );
document.write( "c. How many like none of the three meals<BR>\n" );
document.write( "90-(13+8+5+15+10+13+22) = 90-86 = 4<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );