The Life is a Dance troupe has two choices in how it will be paid for its next series of performances. The first option is to receive $12,500 for the series plus 5% of all ticket sales. The second option is $6,800 for the series plus 15% of ticket sales. The company will perform three consecutive nights in a hall that seats 2,200 people. All tickets will cost $12.

a. How much will the troupe receive under each plan if a total of 3500 tickets are sold for all three performances?
b. Write an equation that gives the amount the troupe will receive under the first plan for any number of tickets sold.
c. Write an equation that gives the amount the troupe will receive under the second plan for any number of tickets sold.
d. How many tickets must the troupe sell for the second plan to be the better choice?
e. Which plan should the troupe choose? Justify your choice.

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Honduran-American dancer Homer Avila performed a solo work titled NotWithout Words in February 2002, one year after losing his leg and part of his hip to cancer