Answer to Question #156544 in Physics for Kaosarat

Question

Each of 39 of my friends has either a dog, a cat or a rabbit. Each of 24 of them has a dog, each of 17 has a cat and each of 16 has a rabbit. The number having both a dog and a cat is 1 more than the number having both a cat and a rabbit. There are 9 who have both a dog and a rabbit while 2 of them have all the three. How many of my friends have both a rabbit and a cat?

Answer 1

$39-24=15$ without dog

$16-9=7$ have rabbit without dog

$15-7=8$ have only cat.

7 cats and 7 rabbits remain. The number having both a dog and a cat is 1 more than the number having both a cat and a rabbit. This is possible provided that there are 3 pairs of (cat+rabbit) and 4 pairs of (dog+cat).

$2(cat+dog+rabbit)+7(dog+rabbit)+$

$+4(dog+cat)+\bold{3(cat+rabbit)}+$

$+11dog+8cat+4rabbit=24+17+16$.

So, three your friends have both a rabbit and a cat. Answer