SOLUTION: 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 Bank

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Question 1209540: 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.
(a) Draw a Venn diagram to illustrate information.
(b) Find the number of students who liked:
(i) Banku and Rice
(ii) only two of the meals
(iii) none of the three meals
Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

Based on this info "13 liked Banku only, 8 Rice only, 5 Fufu only and 22 liked all three meals" we would have this Venn Diagram so far.


Because "The results showed that 63 liked Banku(B), 55 liked Rice(R) and 50 Fufu(F)", we can form this system of equations
system%2813%2Ba%2Bb%2B22+=+63%2Ca%2B8%2B22%2Bc=55%2Cb%2B22%2Bc%2B5=50%29
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:


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

Part (a) is completed at this point.
I'll let the student handle part (b).