An amateur drama group hire a theatre for their production. They expect to sell all 850 tickets, some at $12 and the rest at $8. The group require the ticket sales to cover their $3760 production costs and to make a profit of $4000. If they are to exactly achieve this target and their expectations regarding ticket sales are correct how many of the 850 tickets should they charge $12 for and how many should they charge $8 for?