B3. As Rachel travelled to school, she noticed that, at each bus stop, one passenger got off and $x$ passengers got on, where $x \geq 2$. After five stops, the number of passengers on the bus was $x$ times the number of passengers before the first stop. How many passengers were on the bus before the first stop?
Solution
Let the number of passengers who were on the bus before the first stop be $n$. Then, after five stops, the number of passengers on the bus was $n-5+5 x$. So $n-5+5 x=n x$, that is, $n x-n=5 x-5$. Therefore $n(x-1)=5(x-1)$. Hence $n=\frac{5(x-1)}{x-1}=5$, as $x \neq 1$.

So there were five passengers on the bus before the first stop.