The members of the city cultural center have decided to put on a play once a night for a week. Their auditorium holds 600 people. By selling tickets, the members would like to raise $3 comma 300 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 600 seats are filled for a performance, how many of each type of ticket must have been sold for the members to raise exactly $3 comma 300 ? 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 $3 comma 300 did ticket sales fall?

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Mathematics

24 June, 00:06

The members of the city cultural center have decided to put on a play once a night for a week. Their auditorium holds 600 people. By selling tickets, the members would like to raise $3 comma 300 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 600 seats are filled for a performance, how many of each type of ticket must have been sold for the members to raise exactly $3 comma 300 ? 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 $3 comma 300 did ticket sales fall?

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Katz · Answer 1

A) At $3,300 for 600 seats, the average price per seat is 3300/600 = $5.50. The mix of tickets that results in that average can be found using an X diagram as shown below. The numbers on the right are the differences along the diagonals. When they are multiplied by 2, they add to 600. This shows that the required sales for revenue of $3,300 are

200 adult tickets

400 student tickets

b) When 3 student tickets are sold for each adult ticket, the average seat price is

(3*$4.50 + 7.50) / 4 = $5.25

Then the shortfall in revenue is ...

$3,300 - 480*$5.25 = $780