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Digital SAT
Digital SAT Mathematics - No Calculator Section

Maximizing Revenue at a Movie Theater

Very Hard Heart Of Algebra Linear Equations And Inequalities

At a local movie theater, the relationship between the number of tickets sold, $$x$$, and the total revenue, $$R$$ (in dollars), can be expressed by the equation:

$$R = 10x - 0.5x^2$$

Where the ticket price is $10, and the theater experiences a loss of $0.50 for every ticket sold beyond 20 tickets due to operational costs. If the theater wants to maximize its revenue, how many tickets should it sell?

Hint

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