Question

In a survey of 151 pet owners, 48 said they own a dog, and 95 said they own a cat. 42 said they own both a dog and a cat. How many owned neither a cat nor a dog?

Answer 1

Present the information in diagram

`\begin{gathered} \text{Total pet owners=151} \\ \text{Dog owners, D=48} \\ \text{Cat owners, D=}95 \\ Dog\text{ and cat owners =42} \\ \text{Let the number that own neither =x} \end{gathered}`

Then the venn diagram becomes

Then take the sum of the and equate to the total in the top of the table.

Hence

`\begin{gathered} (95-42)+42+(48-42)+x=151 \\ 53+42+6+x=151 \\ 101+x=151 \end{gathered}`

Subtract 1010 from both sides, we have

`\begin{gathered} 101-101+x=151-101 \\ x=151-101 \\ x=50 \end{gathered}`

Therefore

The number of that owned neither a cat nor a dog is 50