Question

Tickets to a school play cost $2 if bought in advance and $3 at the door. By selling all 400 tickets, $1030 was collected. First write, then solve the equation(s) to find out how many tickets were sold in advance.

Answer 1

170 tickets.

Explanation:

Write formulas for the question.

`N_2+N_3=400`

`2N_2+3N_3=1030`

Then use substitution.

`N_2=-N_3+400`

`2(-N_3+400)+3N_3=1030`

`-2N_3+800+3N_3=1030`

`N_3=230`

So number of $3 tickets sold is 230. But they ask for the tickets bought in advance (i.e. the tickets sold for $2). Use substitution again.

`N_2+230=400\\N_2=400-230\\N_2=170`