In the city of san durango, 60 people own cats, dogs, or rabbits. If 30 people owned cats, 40 owned dogs, 10 owned rabbits, and 12 owned exactly two of the three types of pet, how many people owned all three?
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Answer:
4.
Step-by-step explanation:
Given, Total number of people that own cat, dog or rabbit = 60.
People that own cat = 30 (Let's denote it by C)
People that own dog = 40 (Let's denote it by D)
People that own rabbit = 10 (Let's denote it by R)
Any two of three pets are owned by = 12 people.
So,
Total = C + D + R - (CD+DR+RC) - 2CDR
⇒ 60 = 30 + 40 + 10 - 12 - 2CDR
⇒ 2CDR = 80 - 60 - 12
⇒ 2CDR = 8
⇒ CDR = 4
Therefore, 4 people owned all the three pets.
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