A vet surveys 26 of his patrons. He discovers that 14 have dogs. 10 have cats. 5 have fish. 4 have dogs & cats. 3 have dogs & fish. 1 has a cat & a fish. Use a diagram to answer the following question: If no one has all 3 kinds of pets, how many patrons have none of these pets?
make 3 overlapping circles, label them D, C, and F
4 have dogs and cats, put 4 in the region overlapped by D andC but not F
3 have dogs and fish, put 3 in the region overlapping D and F, but not C
1 has a cat and a fish, put 1 in the region overlapping C and F, but not D
Now look at circle D, we already have a total of 7 in there, but there were 14 that have dogs. So the region of D not overlapping anything is 7
Same way, 5 into rest of C, 1 into rest of F
Add them all up, I get 21
But there were 26 patrons, so 5 did not have any of the 3 kinds of pets
5 didn't
I HATE MATH
whoever Reiny is really explained that well and now i am done with my homework,THANKS Reiny! :)
To answer this question, let's create a diagram called a Venn diagram that represents the different categories of pets the patrons have.
Let's start by drawing three overlapping circles. Label one circle as "Dogs," another as "Cats," and the third one as "Fish." The overlapping regions represent the patrons who have more than one type of pet.
Now, we are given the following information:
- 14 patrons have dogs
- 10 patrons have cats
- 5 patrons have fish
- 4 patrons have both dogs and cats
- 3 patrons have both dogs and fish
- 1 patron has both a cat and a fish
Using this information, we can fill in the overlapping regions in the Venn diagram:
```
Dogs
/ \
/ \
Cats Fish
| |
| |
\ /
\ /
None
```
Let's calculate the number of patrons who have none of these pets:
To find the number of patrons who have none of these three pets, we need to determine the total number of patrons and then subtract the number of patrons in the circles representing dogs, cats, and fish.
We are given that a vet surveys 26 patrons. So, the total number of patrons is 26.
Now, let's find the number of patrons in each circle:
- 14 patrons have dogs
- 10 patrons have cats
- 5 patrons have fish
Next, let's find the overlapping regions:
- 4 patrons have both dogs and cats
- 3 patrons have both dogs and fish
- 1 patron has both a cat and a fish
To find the number of patrons who have none of these pets, we need to subtract the sum of the patrons in the circles and the overlapping regions from the total number of patrons.
Total number of patrons: 26
Number of patrons with dogs: 14
Number of patrons with cats: 10
Number of patrons with fish: 5
Number of patrons with both dogs and cats: 4
Number of patrons with both dogs and fish: 3
Number of patrons with both cats and fish: 1
Number of patrons with none of these pets = Total number of patrons - (Number of patrons with dogs + Number of patrons with cats + Number of patrons with fish - Number of patrons with both dogs and cats - Number of patrons with both dogs and fish - Number of patrons with both cats and fish)
Number of patrons with none of these pets = 26 - (14 + 10 + 5 - 4 - 3 - 1)
Number of patrons with none of these pets = 26 - (26 - 8)
Number of patrons with none of these pets = 26 - 18
Number of patrons with none of these pets = 8
Therefore, 8 patrons have none of these pets.