Question

A class adviser surveyed 35 of his students on what kind of pets they have at home he found out that 15 have dogs 12 have cats and 8 have birds 5 have dogs and cats 4 have dogs and birds and 2 have cats and bids.how many have dogs ONLY

Answer 1

The answer is only 6 have dogs

Explanation:

B + C + D - B∩C - B∩D - C∩D + B∩C∩D + x = 35

8 + 12 + 15 - 2 - 4 - 5 + 0 + x = 35

With Dogs only: 15 - (5+4) = 6

Just in case, we can calculate the others too:

With Cats only: 12 - (5+2) = 5

With Birds only: 8 - (4+2) = 2

With dogs and cats: 5

With birds and dogs: 4

With cats and birds: 2

With dogs, cats, and birds : 0

Total students surveyed: 35

6 + 5 + 2 + 5 + 4 + 2 = 24 students with pets

35 - 24 = 11 students have no pets

Answer 2

Explanation:

With Dogs only: 15 - (5+4) = 6

With Cats only: 12 - (5+2) = 5

With Birds only: 8 - (4+2) = 2

With dogs and cats: 5

With birds and dogs: 4

With cats and birds: 2

With dogs, cats, and birds : 0

Total students surveyed: 35

6 + 5 + 2 +5 + 4 + 2 = 24 students with pets

35 - 24 = 11 students have no pets