A band is performing at an auditorium for a fee of $1500. In addition to this fee, the band receives 30% ofeach $20 ticket sold. The maximum capacity of the auditorium is 800 people.a. Write an equation that represents the band's revenue R when x tickets are sold.An equation is R=B. The band needs 5000 for new equipment so how many tickets need to b sold in order to get enough koney to buy the equipment.

Answer:A. [tex]R=1,500+6x,\ x\le 800[/tex]B. 584Step-by-step explanation:A band is performing at an auditorium for a fee of $1500. In addition to this fee, the band receives 30% of each $20 ticket sold. Let x be the number of tickets sold, then these x tickets cost $20x. Calculate 30% of 20x:[tex]20x\cdot 0.3=6x[/tex]A. The total cost is[tex]R=1,500+6x[/tex]The maximum capacity of the auditorium is 800 people, so x≤800.B. The band needs $5,000 for new equipment so[tex]1,500x+6x\ge 5,000\\ \\6x\ge 3,500\\ \\x\ge \dfrac{3500}{6}\\ \\x\ge 583.333...[/tex]So, it is enough 584 tickets to be sold.