7. 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 Rwhen x tickets are sold.
b. The band needs 5000 for new equipment. How many tickets must be sold for the band to earn enough money to buy the new equipment?
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Answer:
Solution:According to question,Auditorium fee (A): $1500. Ticket price (P): $20. Maximum capacity of the auditorium = 800 peopleProfit gained with each $20 ticket sold= 30%Cost needs for new equipment = $5000Revenue of the band(R) =?Number of Ticket sold (x) =?As we know,Revenue = (percentage of ticket sold *ticket price) + Auditorium feeR=30% of $20 * x + $1500 (by question). = 30/100 * $20 * x + $1500. = 6x + $1500………………………………………………………..equation 1Therefore, the revenue of band when ‘x ‘number of ticket sold is 6x+ $1500.Again, Cost needs for new equipment = $5000 (Given)
R= $1500+ 6x (Putting the value from equation 1)Or, $5000= $1500+ 6x (Putting R= $5000)Or, 6x =5000-1500
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