Could you explain how I would get the residual demand function for this question?

Question: Cinema Paradiso is a movie house in a medium-sized college town. If the theater is open, the owners must pay fixed nightly amount of $500 for films, ushers and so on, regardless of how many people come to the movie. For simplicity, assume that if the theater is closed, its costs are zero. The nightly demand for Cinema Paradiso screenings by students is Qs = 220 40Ps, where Qs is the number of movie tickets demanded by students at price Ps. The nightly demand for non-student moviegoers is qo 140 -20Pn. Suppose that the cinema has a maximum capacity of 150 moviegoers and the manager wants to price discriminate by charging different prices to students and non students. If Qs tickets are sold to students, write an expression for the residual demand that is left for nonstudents. Use this to construct an equation for the price of non-students as a function of the number of student tickets sold. What are Cinema Paradiso's profits as a function of only Qs? Find the profit maximizing number of tickets sales to students and non-students respectively along with the prices charged.