Question

a pet store surveyed 210 people to see how many own a dog 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.)
(a) how many of the people own a dog?
people
(b) how many of the people own neither a dog nor a bird?
people
(c) how many of the people do not own both a dog and a bird?
people

Explanation:

Step1: Calculate the number of people who own a dog

The number of people who own a dog is the sum of those who own only a dog and those who own both a dog and a bird.
$$26 + 87=113$$

Step2: Calculate the number of people who own neither a dog nor a bird

The total number of people surveyed is \(210\). First, find the number of people who own a dog or a bird or both: \(26+87 + 49=162\). Then, the number of people who own neither is \(210-(26 + 87+49)=210 - 162 = 48\)

Step3: Calculate the number of people who do not own both a dog and a bird

The number of people who do not own both is the total number of people minus the number of people who own both. The total number of people is \(210\), and the number of people who own both is \(87\). So it is \(210-87=123\)

Answer:

(a) \(113\) people
(b) \(48\) people
(c) \(123\) people