To determine whether you have enough money to purchase tickets for your family, we need to set up an inequality that accounts for the cost of tickets, the online processing fee, and parking.
-
Determine the variables:
- Let \( t \) be the number of tickets.
- The cost of one ticket is $125.
- The online processing fee per ticket is $5.75.
- The parking fee is $20.
-
Set up the total cost: The total cost for \( t \) tickets can be expressed as: \[ \text{Total Cost} = (125 + 5.75)t + 20 \] Simplifying this gives: \[ \text{Total Cost} = 130.75t + 20 \]
-
Set up the inequality: Since you have $685 to spend, the inequality is: \[ 130.75t + 20 \leq 685 \]
-
Solve the inequality: Subtract 20 from both sides: \[ 130.75t \leq 665 \] Then, divide by 130.75: \[ t \leq \frac{665}{130.75} \approx 5.08 \]
Since \( t \) must be a whole number, you can purchase a maximum of 5 tickets.
Summary:
- Inequality: \( 130.75t + 20 \leq 685 \).
- Maximum number of tickets you can purchase: 5.
Therefore, based on the inequality, yes, you can purchase the tickets (for a family of five).
Correct Choice from Options:
The correct representation is:
- \( 130.75t + 20 \leq 685 \), and yes, you can purchase the tickets (since you can afford 5 tickets).
However, this exact option doesn't appear to be among the choices you provided. The closest one based on the calculations is:
- \( 125t + 5.75t + 20 \leq 685 \), and yes, you can purchase the tickets.
1 answer