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Beginning and Intermediate Algebra

A famous comedian will appear at a comedy club for one performance. The equation $R(p)=-5 p^{2}+300 p$ describes the relationship between the price of a ticket,

$p,$ in dollars, and the revenue, $R,$ in dollars, from ticket sales. That is, the revenue is a function of price.

a) Determine the club's revenue from ticket sales if the price of a ticket is $\$ 40$

b) Determine the club's revenue from ticket sales if the price of a ticket is $\$ 25$

c) If the club is expecting its revenue from ticket sales to be $\$ 4500,$ how much should it charge for each ticket?