Answer:
A. [tex]R=1,500+6x,\ x\le 800[/tex]
B. 584
Step-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.
