Each of the sets A, B and C consist of 23 people each. If the total number of people is 37, how
many people belong to at least two sets?
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Answer:
people belong to at least two sets = 28
Step-by-step explanation:
Each of the sets A, B and C consist of 23 people each.
the total number of people is 37
Total = A + B + C - A∩B - A∩C - B∩C + A∩B∩C
A = B = C =23
Total = 37
A∩B = 2x + x = 3x
A∩C = 1.5x + x = 2.5x
B∩C = 2.5x + x = 3.5x
37 = 23 + 23 + 23 - 3x - 2.5x - 3.5x + x
37 = 69 -8x
=> 8x = 32
=> x = 4
people belong to at least two sets 2x + 1.5x + 2.5x + x = 7x
=> 7*4 = 28
people belong to at least two sets = 28
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