Final answer:
To find the total cost for 13 tickets, two equations were made from the available information. Solving these equations, the ticket price was found to be $32.50, and the processing fee was $11.95. The total cost for 13 tickets was calculated as $434.45.
Step-by-step explanation:
To solve this problem, we need to set up a linear equation based on the information given about the cost of hockey game tickets. We know that the total cost includes a processing fee and a ticket price for each ticket. Let's use P for the processing fee and t for the ticket price.
The cost for 5 tickets is $174.45, so we can write the equation 5t + P = $174.45. Similarly, the cost for 8 tickets is $271.95, which gives us the equation 8t + P = $271.95. We can solve these two equations simultaneously to find the values of t and P.
Subtract the first equation from the second to eliminate P:
8t + P = $271.95
5t + P = $174.45
Subtracting, we get 3t = $97.50. Dividing by 3, we find that t = $32.50.
Now, we can plug value of t into one of the original equations to find P:
5t + P = $174.45
5($32.50) + P = $174.45
$162.50 + P = $174.45
P = $174.45 - $162.50
P = $11.95
With both P and t known, we can find the total cost for 13 tickets:
13t + P = 13($32.50) + $11.95
13t + P = $422.50 + $11.95
Total cost for 13 tickets = $434.45