A team sells two categories of tickets, gold seats and purple seats. Premium fans value gold seats as worth $30 and purple seats as worth $13. Budget fans value gold seats as worth $12 and purple seats are worth $9. There are an equal number of the two fans.

The team sells tickets to the purple seats for $9. To maximize profits, how much should they charge for a gold seat?

Answer is $26, show workings, thanks.