https://file.aiquickdraw.com/mathbot/file/1729637461680oq2mc6w8.jpg

Let's analyze the Venn diagram and solve each part of the question:

### Given data from the Venn diagram:
- 31 people own **only a dog**.
- 45 people own **only a cat**.
- 223 people own **both a dog and a cat**.
- 121 people **do not own** either a dog or a cat.

Now, let's solve the three questions:

### (a) How many of the people own a cat?
To find how many people own a cat, we need to sum the people who own **only a cat** and those who own **both a cat and a dog**.

\[
\text{People who own a cat} = 45 (\text{only a cat}) + 223 (\text{both a cat and a dog}) = 268 \text{ people}.
\]

### (b) How many of the people own a dog or a cat (or both)?
For this, we need to sum all the people who own a dog, a cat, or both. This includes:
- People who own only a dog: 31.
- People who own only a cat: 45.
- People who own both a dog and a cat: 223.

\[
\text{People who own a dog or a cat (or both)} = 31 + 45 + 223 = 299 \text{ people}.
\]

### (c) How many of the people do not own both a dog and a cat?
To answer this, we need to find how many people either own only a dog or only a cat. This would be the sum of:
- People who own only a dog: 31.
- People who own only a cat: 45.

\[
\text{People who do not own both a dog and a cat} = 31 + 45 = 76 \text{ people}.
\]

### Summary:
- (a) 268 people own a cat.
- (b) 299 people own a dog or a cat (or both).
- (c) 76 people do not own both a dog and a cat.

Would you like more details on any of these calculations or any further clarification?

Here are 5 related questions you can explore:
1. How many people own only a dog?
2. What percentage of the surveyed people own a cat?
3. How many people do not own a pet at all?
4. What is the total number of people in the survey?
5. How many people own both a dog and a cat?

**Tip:** In Venn diagrams, intersections represent people or objects shared between sets, so be mindful when counting overlapping groups!

A pet store surveyed 420 people to see how many own a dog and how many own a cat. How many people own a cat, how many own a dog or a cat (or both), and how many do not own both a dog and a cat?

Analyze a Venn diagram based on a survey of 420 people regarding dog and cat ownership. Learn how to calculate the total number of cat owners, people who own either or both pets, and those who do not own both using set theory and arithmetic.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation