how much does each concert ticket cost

Question

3 tickets equal $169.50

5 tickets equal $267.50

9 tickets equal $463.50

12 tickets equal $610.50

Total cost include service fee and only one time service fee

Answer 1

So, it looks like each ticket is the same price as another ticket, and the fee is applied once per purchase.  Is that correct?

 

If so, it doesn't really matter which two purchases you use to set up a system of equations.

I'm calling tickets (t) and the fee (f).

 

Re-writing your scenario, we have:

  3t+f=169.50

  5t+f=267.50

  9t+f=463.50

12t+f=610.50

 

Pick two and solve a system of equations. This can be done about 5 or 6 different ways, so I'll just pick a method for tonight.  I'll use the first two equations.

 

3t+f=169.50 
5t+f=267.50   -->  f=267.50-5t

 

Substitute the f expression in the place of f...

3t+f=169.50

3t+267.50-5t=169.50                                   ... and solve.

-2t+267.50=169.50

267.50-169.50=2t

98=2t

98/2=2t/2

49=t

So, one ticket costs $49.  This hasn't told us how much the fee is, but we still have those equations, so let's check it out.

 

3t+f=169.50

3(49)+f=169.50

147+f=169.50

147+f-147=169.50-147

f=22.50

It looks like the fee is $22.50.  The only thing left to do is to make sure these answers make sense with every original equation.

 

3t+f=169.50   --->   3(49)+22.50=169.50
5t+f=267.50   --->   5(49)+22.50=267.50

9t+f=463.50   --->   9(49)+22.50=463.50
12t+f=610.50 --->  12(49)+22.50=610.50

If each of these equations on the right are correct, then each ticket costs $49 and the fee is $22.50.