Question

the drama club sold 1500 tickets for the end of the year performance. Admission prices were 12 for adults and $6 for students. The total amount collected at the box office was 15480. How many students attended the play?

Answer 1

These are the equations you need - a+k=total, 12a+6k=15480

Answer 2

Set up two equations: one for the amount of money collected, and one for the number of tickets sold (people who attended).

Let a= adults
Let s= students

Money equation:
$15480=12a+6s$

Ticket equation:
$1500=a+s$

Now just solve the system of equations for s:
$15480-12a=6s\\ \frac{15480}{6} - \frac{12a}{6} =s\\ 2580-2a=s\\ 1500=a+s\\ 1500=a+(2580-2a)\\ 1500=-a+2580\\ 1500-2580=-a\\ -1080=-a\\ 1080=a\\ \\ 1500=a+s\\ 1500=1080+s 420=s$

420 Students attended