Tickets to the school prom cost $3 in advance and $4 at the door. 684 people attended and $2457 was collected. How many of each ticket was sold?

Question

Tickets to the school prom cost $3 in advance and $4 at the door. 684 people attended and $2457 was collected. How many of each ticket was sold?

Answer 1

Here's what we know:

a + d = 684 (attendance and door tickets equal 684 sold)

3a + 4d = 2457 (total ticket proceeds equals $2457)

 

Let's solve this through elimination. Multiply the first equation by -3:

-3a - 3d = -2052

3a  + 4d = 2457

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d = 405

 

Now that you know the door tickets, you can use that to find how many advance tickets were sold.