Question

a theater production charges $21 for adult tickets and $15 for student tickets. if the production sold 102 tickets for its opening night and made $1,932 in ticket sales, how many of each type of tickets were sold?

Explanation:

Step1: Define variables

Let \( x \) be the number of adult tickets and \( y \) be the number of student tickets. We know two equations: \( x + y = 102 \) (total tickets) and \( 21x + 15y = 1932 \) (total revenue).

Step2: Solve the system

From the first equation, \( y = 102 - x \). Substitute into the second equation:
\( 21x + 15(102 - x) = 1932 \)
\( 21x + 1530 - 15x = 1932 \)
\( 6x = 1932 - 1530 \)
\( 6x = 402 \)
\( x = \frac{402}{6} = 67 \)

Step3: Find \( y \)

Substitute \( x = 67 \) into \( y = 102 - x \):
\( y = 102 - 67 = 35 \)

Answer:

Adult tickets: 67, Student tickets: 35