a theater production charges $21 for adult tickets and $15 for student tickets. if the production sold 102…
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?
Answer
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