A survey of 132 pet owners yielded the following information: 49 pet owners own fish; 55 own a bird; 50 own a cat; 66 own a dog; 2 own all four; 11 own only fish; 16 own only a bird; 10 own fish and a bird; 21 own fish and a cat; 26 own a bird and a dog; 29 own a cat and a dog; 3 own fish, a bird, a cat, and no dog; 1 owns fish, a bird, a dog, and no cat; 9 own fish, a cat, a dog, and no bird; and 10 own a bird, a cat, a dog, and no fish. How many of the surveyed pet owners have no fish, no birds, no cats, and no dogs?
Question
A survey of 132 pet owners yielded the following information: 49 pet owners own fish; 55 own a bird; 50 own a cat; 66 own a dog; 2 own all four; 11 own only fish; 16 own only a bird; 10 own fish and a bird; 21 own fish and a cat; 26 own a bird and a dog; 29 own a cat and a dog; 3 own fish, a bird, a cat, and no dog; 1 owns fish, a bird, a dog, and no cat; 9 own fish, a cat, a dog, and no bird; and 10 own a bird, a cat, a dog, and no fish. How many of the surveyed pet owners have no fish, no birds, no cats, and no dogs?
Solution 1
The total number of pet owners surveyed is 132. The question provides a breakdown of how many pet owners own each type of pet, as well as combinations of different pets. However, it does not provide a number for pet owners who do not own a fish, bird, cat, or dog.
To find this number, we need to add up all the given numbers of pet owners and subtract this from the total number of pet owners surveyed.
Here's the calculation:
49 (fish owners) + 55 (bird owners) + 50 (cat owners) + 66 (dog owners) - 2 (all four) - 11 (only fish) - 16 (only bird) - 10 (fish and bird) - 21 (fish and cat) - 26 (bird and dog) - 29 (cat and dog) - 3 (fish, bird, cat, no dog) - 1 (fish, bird, dog, no cat) - 9 (fish, cat, dog, no bird) - 10 (bird, cat, dog, no fish) = 103
So, 132 (total pet owners) - 103 (owners of fish, birds, cats, dogs or combinations) = 29
Therefore, 29 of the surveyed pet owners have no fish, no birds, no cats, and no dogs.
Solution 2
The total number of pet owners surveyed is 132. The question provides a breakdown of how many pet owners own each type of pet, as well as combinations of different pets. However, it does not provide a number for pet owners who do not own a fish, bird, cat, or dog.
To find this number, we need to add up all the provided numbers of pet owners and subtract this from the total number of pet owners surveyed.
Here's the calculation:
49 (fish owners) + 55 (bird owners) + 50 (cat owners) + 66 (dog owners) - 2 (all four) - 11 (only fish) - 16 (only bird) - 10 (fish and bird) - 21 (fish and cat) - 26 (bird and dog) - 29 (cat and dog) - 3 (fish, bird, cat, no dog) - 1 (fish, bird, dog, no cat) - 9 (fish, cat, dog, no bird) - 10 (bird, cat, dog, no fish) = 132 - 123 = 9
So, 9 of the surveyed pet owners do not own a fish, bird, cat, or dog.
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