Questions: A pet store conducted a survey to gather information about the types of pets people own. Here are the results: • 692 people were surveyed in all • 448 of the people own a dog • 163 of the people own both a dog and a cat, but don't own a fish • 28 of the people own both a dog and a fish, but don't own a cat • 24 of the people own a cat, but own neither a dog nor a fish • 63 of the people own a fish, but own neither a dog nor a cat • 37 of the people own a dog, but own neither a fish nor a cat • 369 of the people own at least one of these three types of pets (dog, fish, cat) Construct a Venn diagram illustrating these results. Then answer the question. All people in the survey Own a dog Own a fish Own a cat How many of the people don't own a cat?

A pet store conducted a survey to gather information about the types of pets people own. Here are the results: • 692 people were surveyed in all • 448 of the people own a dog • 163 of the people own both a dog and a cat, but don't own a fish • 28 of the people own both a dog and a fish, but don't own a cat • 24 of the people own a cat, but own neither a dog nor a fish • 63 of the people own a fish, but own neither a dog nor a cat • 37 of the people own a dog, but own neither a fish nor a cat • 369 of the people own at least one of these three types of pets (dog, fish, cat) Construct a Venn diagram illustrating these results. Then answer the question. All people in the survey Own a dog Own a fish Own a cat How many of the people don't own a cat?
Transcript text: A pet store conducted a survey to gather information about the types of pets people own. Here are the results: • 692 people were surveyed in all • 448 of the people own a dog • 163 of the people own both a dog and a cat, but don't own a fish • 28 of the people own both a dog and a fish, but don't own a cat • 24 of the people own a cat, but own neither a dog nor a fish • 63 of the people own a fish, but own neither a dog nor a cat • 37 of the people own a dog, but own neither a fish nor a cat • 369 of the people own at least one of these three types of pets (dog, fish, cat) Construct a Venn diagram illustrating these results. Then answer the question. All people in the survey Own a dog | Own a fish Own a cat How many of the people don't own a cat?
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Solution

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Solution Steps

Step 1: Identify the total number of people surveyed
  • The problem states that 92 people were surveyed.
Step 2: Calculate the number of people who own each type of pet
  • 63% of the people own a dog: \( 0.63 \times 92 = 57.96 \approx 58 \)
  • 18% of the people own both a dog and a cat, but don’t own a fish: \( 0.18 \times 92 = 16.56 \approx 17 \)
  • 14% of the people own both a dog and a fish, but don’t own a cat: \( 0.14 \times 92 = 12.88 \approx 13 \)
  • 7% of the people own both a cat and a fish, but don’t own a dog: \( 0.07 \times 92 = 6.44 \approx 6 \)
  • 10% of the people own all three pets: \( 0.10 \times 92 = 9.2 \approx 9 \)
  • 24% of the people own neither a dog nor a fish: \( 0.24 \times 92 = 22.08 \approx 22 \)
Step 3: Calculate the number of people who own only one type of pet
  • People who own only a dog: \( 58 - 17 - 13 - 9 = 19 \)
  • People who own only a cat: \( 22 - 6 - 9 = 7 \)
  • People who own only a fish: \( 92 - 58 - 7 - 9 = 18 \)

Final Answer

  • Number of people who own only a dog: 19
  • Number of people who own only a cat: 7
  • Number of people who own only a fish: 18
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