The San Francisco Shorties and Oakland Non$-$Athletics are baseball teams located about $20$ miles away from each other's ballparks. The number of tickets sold by either team depends on the price of its own tickets and the price of the other team's tickets. Let $P_S$ and $P_O$ represent the per$-$unit price for each city's respective tick$$ts$.$ Demand for San Francisco's tickets is given by the equation $q_s=170\mathrm{.}00-2P_s+P_o,$ while demand for Oakland's tickets is given by the equation $q_o=340\mathrm{.}00-2P_o+P_s.$

The marginal cost of an extra fan visiting the stadium is zero for both teams. Assume there are no fixed costs. If each team believes the other team's price is independent of its own price choice and each team sets its own price to maximize revenue, what price does each team charge per ticket?

San Francisco's per$-$ticket price $(P_S)$ :

S

Oakland's per$-$ticket price $(P_O)$ :

$