https://file.aiquickdraw.com/mathbot/file/1726106974645dqgffacy.jpg

The problem in the image involves determining the correct equation to represent a situation where Arjun and Emilia purchase tickets to a play. 

### Breakdown:
- **Arjun** purchased 5 tickets at price $ t $ each, and paid an additional online service fee of $3.50 per ticket.
  So, Arjun's total cost is: 
  \[
  5t + 5(3.50) = 5t + 17.50
  \]
  
- **Emilia** purchased 3 tickets at the same price $ t $, but she also paid twice as much for her tickets and was charged an additional service fee of $2.75 per ticket. Emilia's total cost is:
  \[
  3(2t) + 3(2.75) = 6t + 8.25
  \]

Since they spent the same amount, we set their total costs equal to each other:
\[
5t + 17.50 = 6t + 8.25
\]

### Solving:
\[
5t + 17.50 = 6t + 8.25
\]
Subtract $5t$ from both sides:
\[
17.50 = t + 8.25
\]
Subtract 8.25 from both sides:
\[
t = 9.25
\]

Thus, the cost of each of Arjun’s tickets is $9.25.

### Correct Answer:
The correct option that represents this solution is the third one:
- $5(t + 3.5) = 3(2t + 2.75)$, with each ticket costing **$9.25**.

Would you like more details on any step?

### Related Questions:
1. What if Emilia had paid three times as much for her tickets?
2. How would the equation change if Arjun had bought 6 tickets instead of 5?
3. What if Emilia’s service fee was reduced to $1 per ticket?
4. Can you explain how to derive the equation directly from the word problem?
5. What is the significance of the equation equality in such problems?

**Tip**: Always write down what each variable represents before setting up your equations.

Arjun purchased 5 tickets to a play, and Emilia purchased 3 tickets. Arjun paid $3.50 per ticket in service fees, and Emilia paid twice as much per ticket, with a $2.75 service fee. Both spent the same amount. What is the cost of Arjun's tickets?

Solve the equation representing the cost of tickets purchased by Arjun and Emilia, where Arjun paid service fees of $3.50 per ticket, and Emilia paid twice as much with a $2.75 service fee. Learn to find the cost of Arjun's tickets using algebraic equations. Suitable for Grades 7-9.

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