Please show all your work if possible and label the answer. Thank you.

Consider a Broadway theater with 500 seats, divided into orchestra, balcony, and main seating. Orchestra seats sell for $50, balcony seats for $25, and main seats for $35. If all the seats are sold, the gross revenue to the theater is $15,000. If all the main and balcony seats are sold, but only half the orchestra seats are sold, the gross revenue is $14,000. One may ask: how many seats are there of each kind? SET UP a system of equations that could help solve the above problem. You must clearly: 1) define any variable used and 2) write each relevant equation