set up system of equations

Question

The theater department at the University of Alabama has collected the reciepts for a production of Phantom of the Opera, which totals $1030. The ticket prices were $3.50 for students, $5.00 for adults, and $2.50 for children. Twice as many adults attended as children, ant the number of students that attended was 20 more than one-half the number of adults. Find the number of tickets sold to adults, students, and children. Set up a system of linear equations that models the problem as described. Clearly define the unknowns in the context of the problem.

Answer 1

Let s = the number of student tickets

Let a = the number of adult tickets

Let c = the number of childr er n's tickets

 

3.5s + 5a + 2.5c = 1030

a = 2c

s = a/2 + 20