A4. In the first week after his birthday, Bill's uncle gave him some money for his piggy bank. Every week after that Bill put $£ 2$ into his piggy bank. At the end of the ninth week after his birthday Bill had trebled the amount he started with. How much did he have in total at the end of the ninth week?
Solution
$£ 24$

Let the amount Bill's uncle gave him in the first week after his birthday be $£ x$. Every week after that Bill put $£ 2$ into his piggy bank and so by the end of the ninth week Bill had added $£ 16$ in total to his piggy bank. Therefore, the total amount in his piggy bank at the end of the ninth week was $£(x+16)$. Also, by the end of the ninth week, Bill had trebled the amount he started with and so $(x+16)=3 x$, which gives $x=8$.
Therefore, Bill had $£ 24$ in total at the end of the ninth week.