The members of the city cultural center have decided to put on a play once a night for a week. Their auditorium holds a total of 500 people. By selling tickets, the members would like to raise
$3150 every night to cover all of their expenses. Let x represent the number of adult tickets sold at
$7.50 each. Let y represent the number of students tickets sold at $4.50 each.

a. Write a linear equation that models the $3150 income that the members hope to raise from the
sale of the adult and student tickets each night.

b. Write a second linear equation that models the number of adult and student tickets they sell if all
500 seats are sold for a single night’s performance.

c. Use your preferred method to solve the system if all 500 seats are filled for a performance, how
many of each ticket must be sold so that the members raise exactly $3150.