Library collections after new deliveries

A school library has \(720\) fiction and non-fiction books altogether. After \(40\) fiction books and \(80\) non-fiction books are delivered, the ratio of fiction to non-fiction books becomes \(13:8\). Let \(f\) and \(n\) be the original numbers of fiction and non-fiction books respectively.

1. Using the original total, form an equation in \(f\) and \(n\).[1]
2. Using the ratio after the delivery, form another equation in \(f\) and \(n\).[2]
3. Hence, solve the simultaneous equations obtained in (a) and (b) and find the original numbers of fiction and non-fiction books.[3]