Matrix question

Question

On July 7, 2004, Shania Twain was scheduled to perform at the TD Waterhouse Centre in Orlando, Florida. The center offered 18,039 seats for the concert in three seating classifications: floor, lower, and upper. Based upon their location, tickets were offered at three different prices: $80, $65, and $45.† Suppose the average price of a floor ticket was $80, the average price of a lower ticket was $65, and the average price of an upper ticket was $45. If concert planners expected a total of 15,000 tickets would be sold, including 5 times as many tickets on the lower level as on the floor, how many of each type of ticket would have to be sold to reach $877,500 in ticket revenue?

Answer 1

number of tickets sold for:

floor = F

lower = L

upper = U

F + L + U = 15,000 (1)

and

80F + 65L + 45U = 877,500 (2)

L = 5F (3)

write (3) in (1) for L

F + 5F + U = 15,000

U = 15,000 - 6F (4)

write (3) and (4) in (2) for L and U

80*F + 65*5*F + 45*(15,000 - 6*F) = 877,500

80F + 325F + 675,000 - 270F = 877,500

135F = 202,500

F = 1,500

L = 5F = 5*1,500 = 7,500

U = 15,000 - 6F = 15,000 - 6*1,500 = 6,000