Question

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. 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 1

A.
`R=1,500+6x,\ x\le 800`

B. 584

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:

`20x\cdot 0.3=6x`

A. The total cost is

`R=1,500+6x`

The maximum capacity of the auditorium is 800 people, so x≤800.

B. The band needs $5,000 for new equipment so

`1,500x+6x\ge 5,000\\ \\6x\ge 3,500\\ \\x\ge (3500)/(6)\\ \\x\ge 583.333...`

So, it is enough 584 tickets to be sold.