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