Question 1209540
<font color=black size=3>
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.
{{{
drawing(400,400,-5,5,-5,5,
line(-4,4,4,4),
line(4,4,4,-4),
line(4,-4,-4,-4),
line(-4,-4,-4,4),

circle(-1,1,2),circle(1,1,2),circle(0,-0.7321,2),

locate(-2.8-0.5,2.8,Banku),
locate(2.6,2.8,Rice),
locate(1,-2.6,Fufu),
locate(-2,1.8,13),
locate(0,1.8,a),
locate(2,1.8,8),
locate(-1.5,0,b),
locate(0,0.4,22),
locate(1.2,0,c),
locate(0,-1.5,5),
locate(3,-1.5,d)
)
}}}


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
{{{system(13+a+b+22 = 63,a+8+22+c=55,b+22+c+5=50)}}}
Each equation is the result of adding the numbers in the circles shown.
Solving this system leads to a = 15, b = 13, c = 10. 
I'll let the student handle the scratch work.


If we plug in those a,b,c values then we get:
{{{
drawing(400,400,-5,5,-5,5,
line(-4,4,4,4),
line(4,4,4,-4),
line(4,-4,-4,-4),
line(-4,-4,-4,4),

circle(-1,1,2),circle(1,1,2),circle(0,-0.7321,2),

locate(-2.8-0.5,2.8,Banku),
locate(2.6,2.8,Rice),
locate(1,-2.6,Fufu),
locate(-2,1.8,13),
locate(0,1.8,15),
locate(2,1.8,8),
locate(-1.5,0,13),
locate(0,0.4,22),
locate(1.2,0,10),
locate(0,-1.5,5),
locate(3,-1.5,d)
)
}}}


Adding up all the values in the Venn Diagram should get us 90 total students.
13+15+8+13+22+10+5+d = 90
86+d = 90
d = 90-86
d = 4


The completed Venn Diagram is
{{{
drawing(400,400,-5,5,-5,5,
line(-4,4,4,4),
line(4,4,4,-4),
line(4,-4,-4,-4),
line(-4,-4,-4,4),

circle(-1,1,2),circle(1,1,2),circle(0,-0.7321,2),

locate(-2.8-0.5,2.8,Banku),
locate(2.6,2.8,Rice),
locate(1,-2.6,Fufu),
locate(-2,1.8,13),
locate(0,1.8,15),
locate(2,1.8,8),
locate(-1.5,0,13),
locate(0,0.4,22),
locate(1.2,0,10),
locate(0,-1.5,5),
locate(3,-1.5,4)
)
}}}
Part (a) is completed at this point. 
I'll let the student handle part (b).
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