Answer
(a.) Sold $ = 6550 $,
Supply $ = 6250$.
(b.) Ticket price $ =\$ 60 $,
Tickets supplied and sold $ = 6300 $.
Work Step by Step
Demand model $ N=-25p+7800 $ ... (1).
Supply model $ N=5p+6000 $ ... (2).
Where, $ p= $ dollars per ticket and $N$ is number of tickets.
(a.)
Substitute $ p=\$ 50 $ in equation (1) and (2).
Demand model :-
$ N=-25(50)+7800 $
$ N= -1250+7800 $
$ N= 6550 $
Supply model :-
$ N=5(50)+6000 $
$ N=250+6000 $
$ N=6250 $
Hence, at $ \$ 50 $ per ticket, $ 6550 $ tickets can be sold and $ 6250 $ tickets can be supplied.
(b.)
Equate equation (1) and (2).
$ -25p+7800 =5p+6000 $
$ 7800 - 6000 = 5p+25p $
$ 1800 = 30p $
$ 60 = p $
Substitute the above value into equation (1).
$ N=-25(60)+7800 $
$ N= -1500+7800$
$ N =6300 $.
