System of equations with 3 unknowns

Question

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

120 Preferred

340 Reserved

140 Lawn seats

they sum to 600 total seats

120(80) + 340(60) +140(25) = 33500

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