problem with pupils and find the number of the pupils -arithmetic

Question

In a classroom there are 28 pupils. 19 pupils know to speak English ad 16 pupils speak French. Knowing that every children is speaking at least one language(English or French) find out the number of pupils who are speaking only English.

Thanks:)

Answer 1

Let $e$ denote the number of pure English speakers. Let $f$ denote the number of pure french speakers. Let $m$ denote the number of mixed speakers. Then we have the simultaneous equations $$\begin{align} m + e = 19 \\m + f = 16\\ m + f + e = 28\end{align}$$ From which you immediately get $e=12,\ f=9$ and $m=7$.