A concert venue sells two types of tickets for its performances. The venue's total ticket sales for last night's show...

1. TRANSLATE the equation components

• Given equation: \(\mathrm{12.50x + 18.75y = 8,742.50}\)
• Where:
  • \(\mathrm{x}\) = number of general admission tickets sold
  • \(\mathrm{y}\) = number of VIP tickets sold
  • \(\mathrm{8,742.50}\) = total ticket sales in dollars

2. INFER what coefficients represent in context

• In equations modeling real-world situations, coefficients typically represent rates or unit prices
• Since \(\mathrm{x}\) represents the quantity of general admission tickets, its coefficient (\(\mathrm{12.50}\)) must represent the price per general admission ticket
• Since \(\mathrm{y}\) represents the quantity of VIP tickets, its coefficient (\(\mathrm{18.75}\)) must represent the price per VIP ticket

3. TRANSLATE the question to identify what we need

• The question asks for "the price, in dollars, of each general admission ticket"
• This means we need the unit price for general admission tickets
• From our analysis, this is the coefficient of \(\mathrm{x}\), which is \(\mathrm{12.50}\)

Answer: A (12.50)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students confuse the coefficient (\(\mathrm{12.50}\)) with the term (\(\mathrm{12.50x}\))

Students might think that since \(\mathrm{12.50x}\) represents something related to general admission tickets, this entire expression must be the price. However, \(\mathrm{12.50x}\) represents the total revenue from general admission tickets (price × quantity), not the unit price.

This may lead them to select Choice B (12.50x)

Second Most Common Error:

Poor TRANSLATE reasoning: Students mix up which coefficient goes with which ticket type

Students might focus on the larger coefficient (\(\mathrm{18.75}\)) thinking it's more important, or simply grab the wrong coefficient without carefully tracking which variable represents general admission tickets.

This may lead them to select Choice C (18.75)

The Bottom Line:

This problem tests whether students can distinguish between different components of a linear equation and understand what each represents in context. The key insight is recognizing that coefficients represent unit rates, not total amounts.