I need help with an Algebra 2 question!?

Question

Tickets to a local movie were sold at $6.00 for adults and $4.50 for students. If 75 tickets were sold for $412.50, how many tickets of each type were sold?

I want an answer to this question. The correct answer. Show me how you worked out this problem step by step. If you have a source, please show me what website you got it from. Thanks.

Answer 1

Set up a system of equations to represent the situation:
x = adult tickets
y = student tickets

6x + 4.5y = 412.50       to represent the total price
x + y = 75                       to represent the # sold
     multiply by 6 on both sides of the second equation
Since you multiplied by the same thing that means you didn't change anything.
      6x + 6y = 450

Now, subtract the two equations. You eliminate x and you can solve for y!
       4.5y - 6y = 412.5 - 450
       -1.5y = -37.5
               y = 25

This means that 25 student tickets were sold.
So, x + 25 = 75    meaning x = 75 - 25 = 50 adult tickets were sold.

25 student tickets
50 adult tickets

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