Final answer:
To find the total cost to order 12 tickets, first determine the processing fee from the cost of 5 tickets ($174.45), then write the linear equation incorporating the cost per ticket ($71.95) and the processing fee. The correct linear equation is the total cost equals the processing fee ($185.30) plus 12 times the cost per ticket.
Step-by-step explanation:
To write a linear equation to find the total cost to order 12 tickets for a hockey game when the cost for 5 tickets is $174.45 and the cost for each ticket is $71.95, we need to determine the processing fee first.
Let's denote the processing fee as P and the cost per ticket as T. Since we know the cost for 5 tickets, the equation representing this known total cost would be:
5T + P = $174.45
We are given that the cost per ticket (T) is $71.95, so we can substitute that value into our equation:
5($71.95) + P = $174.45
This simplifies to:
$359.75 + P = $174.45
To find P, we subtract $359.75 from both sides of the equation:
P = $174.45 - $359.75
P = -$185.30
The negative value indicates that we've made a mistake, as processing fees cannot be negative. Let's correct our calculations:
$359.75 - $174.45 = P
P = $185.30
Now, we have the processing fee. The equation to find the total cost for x number of tickets would then be:
Total Cost = P + xT
For 12 tickets, replace x with 12:
Total Cost = $185.30 + 12($71.95)
This is the linear equation that can be used to determine the total cost for 12 tickets.