Question

a pet store surveyed 420 people to see how many own a cat and how many own a bird.
the venn diagram below shows the results. (each number gives the number of people who fall into that venn diagram category.)
all people in the survey
(a) how many of the people own a bird?
(b) how many of the people own a cat or a bird (or both)?
(c) how many of the people do not own both a cat and a bird?

Explanation:

Step1: Find the number of people who own a bird(a)

To find the number of people who own a bird, we add the number of people who own only a bird and the number of people who own both a cat and a bird.
The number of people who own only a bird is \( 188 \), and the number of people who own both is \( 57 \).
So, \( 188+57 = 245 \)

Step2: Find the number of people who own a cat or a bird (or both)(b)

To find the number of people who own a cat or a bird (or both), we add the number of people who own only a cat (\( 96 \)), the number of people who own only a bird (\( 188 \)), and the number of people who own both (\( 57 \)).

$$96 + 188+57=341$$

Step3: Find the number of people who do not own both a cat and a bird(c)

The total number of people surveyed is \( 420 \). The number of people who own both a cat and a bird is \( 57 \).
To find the number of people who do not own both, we subtract the number of people who own both from the total number of people surveyed.
\(420 - 57=363\)

Answer:

(a) \( 245 \) people
(b) \( 341 \) people
(c) \( 363 \) people