Planning a fund-raising dinner, Original Plan, New Deluxe event Plan, Tickets that must be sold for the more deluxe event in order for it to yield the same profit as the original plan.
County Museum is planning a fund-raising dinner. The initial plan was to charge $100/ticket. Catering costs would be $40/plate. Rent of the facility would be $4,000 for the event, and paid staffers (not counting volunteers) would cost $1,000. A string quartet would provide dinner music for $2,000. It is expected that 400 persons would attend this dinner.
A new plan has been put forward for a more deluxe event, with tickets costing $160. Catering for the more elaborate dinner would run $70/plate. Bigger "name" entertainment would be hired instead of the strings, costing $5,000. Paid staff would double in order to provide better service. How many tickets must be sold for the more deluxe event in order for it to yield the same profit as the original plan? [Note that the answer must be a whole number, as fractional tickets are not sold].