Can you please help me with this story problem?

Question

A school has 1200 students. Within a group of 416 students, each person owns a dog or a cat or both. If there are 316 dog owners and 280 cat owners, how many of the dog owners own no cat???

***Please help me solve this as logical as possible***

I have another question waiting for 10 more points waiting to be earned.

Answer 1

Given all 416 own one, the other, or both, then we can solve this very easily.  if you figure that 316 own dogs, then 416-316 equals 100, so 100 only own cats.  then you figure out the reverse.  416-280 equals 136.  So 136 people only own dogs.  I hope I helped.

Answer 2

I think there are 136 people with only dogs.

416 have dogs/cats/both.

596 people have dogs and cats so 596- 416 = 180 people with both.

So if you minus the number of people with cats and dogs (180) from the number of people with dogs in general (316) you should get 136.

Hope I helped.

**Edit: I think the 1200 students is just there as the universal group, so if the question had asked how many peole have NO pets then the 1200 would be relevant.  In this case it isn't.

Answer 3

This is a Venn diagram problem. Draw two overlapping circles, one labeled Dogs, the other Cats. Put an X in the overlapping region. (The number of people who own both. Put 316-X in the Dogs only part of the Dog circle and 280 -X in the Cats only part of the Cats circle.

(316 - X) +X +(280- X) =416

596 - X =416

X =180

316 -180 =136 dog owners with no cat

Answer 4

There should be 136 people with only dogs. The 1200 is irrelevant to the problem, it just shows what kind of group they were pulled from.

Of the 416, all of them own either a dog, cat or both, so if you subtract all the cat owners from the 416, you are left with the ones who own only dogs. 136