The owner of the sole stage-theatre in the city of Vordervilla has found through   experience that the cost of running his 600-seat theatre remains virtually the same irrespective of whether there is a 'full house' or not. 

The owner wishes to maximise his profits and has estimated that the demand curve of adults for the theatre can be represented by the function Q_A = 1000 - 50P, whereas the demand curve of children is given by Q_C = 600 - 50P.

Assume that the owner chooses not to price discrimination and must therefore sell all tickets at the same single price.  What will that price be per ticket?  What will be the ratio of adults to children attending the theatre?