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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.

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rtankus

Answer:

170 tickets.

Step-by-step explanation:

Write formulas for the question.

[tex]N_2+N_3=400[/tex]

[tex]2N_2+3N_3=1030[/tex]

Then use substitution.

[tex]N_2=-N_3+400[/tex]

[tex]2(-N_3+400)+3N_3=1030[/tex]

[tex]-2N_3+800+3N_3=1030[/tex]

[tex]N_3=230[/tex]

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.

[tex]N_2+230=400\\N_2=400-230\\N_2=170[/tex]

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