Question

For a USC home game, ticketmaster charges $45 per ticket, plus a convenience charge of $3.50

per ticket. You must also pay a processing fee of $5.50 on the order. Tim spent $199.50 for his

family to go to the USC game.



Write an equation to model the situation. Use "t" as your variable.




How many tickets did he purchase?

Answer 1

To model the situation, we start by defining \( t \) as the number of tickets Tim purchased. The total cost for the tickets can be calculated as follows:

1. The cost per ticket is $45.
2. The convenience charge per ticket is $3.50.
3. There is an additional processing fee of $5.50 for the order.

The total cost for \( t \) tickets can be expressed with the following equation:

\[
\text{Total Cost} = (\text{Cost per ticket} + \text{Convenience charge per ticket}) \times t + \text{Processing fee}
\]

Substituting the values into the equation gives us:

\[
199.50 = (45 + 3.50)t + 5.50
\]

Simplifying the equation:

\[
199.50 = 48.50t + 5.50
\]

Now, we can isolate \( t \) by subtracting the processing fee from both sides:

\[
199.50 - 5.50 = 48.50t
\]

\[
194.00 = 48.50t
\]

Next, we divide both sides by 48.50 to solve for \( t \):

\[
t = \frac{194.00}{48.50} \approx 4
\]

So, Tim purchased **4 tickets**.