can u help me plz with an ALGEBRA II problem?

Question

in a community of 416 people, 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. thx

Answer 1

416 - 316 = 100
280 - 100 = 180
316 - 180 = 136
136
a hundred dont have a dog
136 dont have a cat
136 - 100 = 36
36

Answer 2

First give out all the dogs. If there are 416 people and 316 dogs, 100 people will be left without a dog. If each person has a dog or a cat, the 100 people without dogs must have a cat. So after giving a cat to the 100 people without a dog the remaining 180 cats must be given to a dog owner.

If 180 dogs owners have a cat, then 316 - 180 or 136 have no cat.

Answer 3

Let's set this problem up:
b = owners who own cats and dogs
d = owners who own just dogs
c = owners who own just cats

There are three equations (not in any order)
1) 416 = b + c + d
2) 316 = b + d
3) 280 = b + c

you can plug equation 2 into equation 1 and see that c = 100. Plug c=100 into equation 3 gives b=180. Using b=100 into equation 2 gives d=136.

The question asks how many of the dog owners own no cat. This means just dog owners. So we can see variable d is what they're looking for. There are 136 catless dog owners.

Answer 4

The Formula for this type of problems is,
n(a intersection b) = n(a) + n(b) - n( a U b )

Here,
n(a) = No. of people having dogs = 316
n(b) = No. of people having cats = 280
n( a U b ) = Total no. of people = 416
n(a intersect b) = No. of people having both dog and cat.

Therefore,
n( a intersect b ) = 316 +280 - 416 = 180

Therefore no. of dog owners who dont gave a cat =
316 - 180 = 136

Answer 5

c = number of cat owners
d = number of dog owners

c = 280
d = 316

(No c) = 416 - c = 416 - 280 = 136

The number of dog owners who own no cat is 136.

Answer 6

100 don't have a dog
136 don't have a cat
36 dog owners have no cat