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Graham Campos
09/29/2024 · High School

Challenge The members of the city cultural center have decided to put on a play once a night for a week. Their auditorium holds 500 people. By selling tickets, the members would like to raise \( \$ 2,850 \) every night to cover all expenses. Let d represent the number of adult tickets sold at \( \$ 7.50 \). Let s represent the number of student tickets sold at \( \$ 4.50 \) each. If all 500 seats are filled for a performance, how many of each type of ticket must have been sold for the members to raise exactly \( \$ 2,850 \) ? At one performance there were three times as many student tickets sold as adult tickets. If there were 480 tickets sold at that performance, how much below the goal of \( \$ 2,850 \) did ticket sales fall?

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The members must sell 200 adult tickets and 300 student tickets to raise exactly \( \$ 2,850 \). In a performance with three times as many student tickets as adult tickets and a total of 480 tickets, the revenue was \( \$ 2520 \), falling \( \$ 330 \) below the goal.

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