Math problem need help

Question

1. A local concert venue has a total of 600 seats. These seats sell at three different prices: $80 for preferred seating, $60 for reserved seating, and $25 for lawn seating. The alternative band, Fishing on Tuesdays, recently sold out the venue and the total revenue collected was $33,500. In contrast, the heavy metal band, Meat Cereal, sold out the preferred seats, but only sold 3/5 of the reserved seats and 4/5 of the lawn seats. The Meat Cereal concert brought in a total revenue of $24,640. How many of each type of seat does the concert venue have?

Answer 1

P+R + L = 600

80P + 60R + 25L = 33,500

16P + 12R + 5L = 6,700

5P + 5R + 5L = 3,000

11P + 7R = 3,700

80P +(3/5)60R+(4/5)25L = 24,640

80P+36R + 20L = 24,640

20P+9R +5L = 6,160

5P +5R +5L = 3,000

15P +4R = 3,160

105P + 28R = 22,120

44P + 28R = 14,800

61P = 7,320

P = 7320/61 = 120 seats in Preferred

4R = 3160-15(120) =3160-1800 = 1360

R = 1360/4 = 340 seats in Reserved

L = 600-340-120 = 140 seats in Lawn

120 Preferred, 340 Reserved, 140 Lawn

check the answers

80(120)+60(340) +25(140) = 9600+ 20400 + 3500 =33500

80(120) 60(3/5)340)+ 25(4/5)140 = 9600+12240+2800 =24640