Question

Tickets to a school play cost $3 for students and $8 for adults. On opening night, $1000 was collected and 150 tickets sold. How many of each kind of ticket were sold? Write a system of equations and use substitution to solve.

Answer 1

Let the number of students who bought tickets be s,
Let the number of adults who bought tickets be a,

Equation 1:

$3s \: + \: 8a \: = \: 1000$

Equation 2:

$s \: + \: a \: = \: 150 \\ s \: = \: 150 \: - \: a$

Substitute ( 2 ) into ( 1 ),

$3(150 \: - \: a) \: + \: 8a \: = \: 1000 \\ 450 \: - \: 3a \: + \: 8a \: = \: 1000 \\ 5a \: = \: 550 \\ a \: = \: 110$

Substitute a = 110 into ( 2 ),

$s \: + \: 110 \: = \: 150 \\ s \: = \: 40$

Ans: 40 Student Tickets, 110 Adult Tickets