A theater sold tickets for a charity event and collected a total of $450 in revenue. The theater sold x...

1. TRANSLATE the problem information

• Given information:
  • Theater collected $450 total revenue
  • x adult tickets at $18 each
  • y student tickets at $12 each
  • Equation: \(\mathrm{18x + 12y = 450}\)

• What each symbol means:
  • \(\mathrm{x}\) = number of adult tickets sold
  • \(\mathrm{y}\) = number of student tickets sold
  • 18 = price per adult ticket
  • 12 = price per student ticket

2. INFER what each term in the equation represents

• Since Revenue = Price × Quantity:
  • \(\mathrm{18x}\) = $18 × x tickets = total revenue from adult tickets
  • \(\mathrm{12y}\) = $12 × y tickets = total revenue from student tickets
  • \(\mathrm{18x + 12y}\) = total revenue from all tickets = $450

• Therefore, \(\mathrm{12y}\) specifically represents the total revenue from student tickets

Answer: C (The total revenue from student tickets)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students focus only on what y represents (number of student tickets) without recognizing that \(\mathrm{12y}\) is a product of price and quantity.

They see "y = student tickets" and think "\(\mathrm{12y}\) must also mean student tickets," not realizing that multiplying by 12 changes the meaning from quantity to revenue. This leads them to select Choice A (The number of student tickets sold).

Second Most Common Error:

Conceptual confusion about revenue vs. quantity: Students don't clearly distinguish between counting tickets and calculating money earned.

They understand that y is student tickets but fail to recognize that when you multiply the number of tickets by the price per ticket, you get the total money (revenue) from those tickets. This causes them to get stuck and guess between choices A and C.

The Bottom Line:

This problem tests whether students can distinguish between a variable (\(\mathrm{y}\) = number of tickets) and a coefficient times that variable (\(\mathrm{12y}\) = revenue from tickets). Success requires carefully translating what each mathematical expression means in the real-world context.