Question

In a survey of 137 pet owners, 36 said they own a dog, and 99 said they own a cat. 31 said they own both a dog and a cat. How many owned neither a cat nor a dog?

Answer 1

Solution

- To solve this question, we need to apply the formula below:

$\text{ Total people in survey }=\text{ Dog owners + Cat owner-Cat and Dog owners +Those that own neither.}$

- We have been given:

$\begin{gathered} \text{ Total people in survey}=137 \\ \text{ Dog owners}=36 \\ \text{ Cat owners}=99 \\ \text{ Cat and Dog owners}=31 \end{gathered}$

- Thus, we can apply the formula above to find those that have neither cats nor dogs.

- This is done below:

$\begin{gathered} 137=36+99-31+X\text{ \lparen where, }X\text{ represents those who own neither dogs nor cats\rparen} \\ 137=104+X \\ \text{ Subtract 104 from both sides} \\ \therefore X=137-104 \\ \\ X=33 \end{gathered}$

Final answer

The number of people that own neither cat nor a dog is 33