[Math] 100 households are surveyed, 60 have cats and 40 have dogs whilst 20 have neither a car or dog. How many households have only cats

Question

100 households are surveyed on a street.
60 have cats, 40 have dogs and 20 have neither a car or dog.
How many households have only a cat?

If you could please show all working out it would be appreciated.

Also (and I apologize if this is a dumb question) would it be possible to work this out using algebra?

Edit: I have attempted this and got 40 but I'm not 100 percent sure I'm correct.

Answer 1

Let $C$ be the number of houses with only cats; $D$, only dogs; $B$, both; and $N$, none.

$\begin{align}C+B&=60\\ D+B&=40\\ N&=20\\ C+D+B+N&=100 \end{align}$

Now you have four equations and four equations, so it's easily solvable now. The answer will be $C$.