A company that creates and sells tape dispensers calculates its monthly profit, in dollars, by subtracting its fixed monthly costs,...

1. TRANSLATE the problem information

• Given information:
  • Equation: \(\mathrm{15,000 = 2.00x - 4,500}\)
  • \(\mathrm{x}\) = number of tape dispensers created and sold
  • Monthly profit = monthly sales revenue - fixed monthly costs
• What this tells us: We need to match each part of the equation to the business formula

2. INFER the equation structure

• Since \(\mathrm{profit = revenue - fixed\ costs}\), our equation must follow this pattern
• Looking at \(\mathrm{15,000 = 2.00x - 4,500}\):
  • 15,000 represents the monthly profit
  • The subtraction structure means: [revenue] - [fixed costs] = profit
  • Therefore: \(\mathrm{2.00x}\) must be revenue, and 4,500 must be fixed costs

3. TRANSLATE what \(\mathrm{2.00x}\) represents

• Since \(\mathrm{x}\) = number of dispensers sold
• And \(\mathrm{2.00x}\) = total monthly sales revenue
• This means \(\mathrm{2.00x}\) represents "the monthly sales revenue, in dollars, from selling \(\mathrm{x}\) tape dispensers"

Answer: A

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE reasoning: Students confuse \(\mathrm{2.00x}\) (total revenue from \(\mathrm{x}\) dispensers) with 2.00 (revenue per single dispenser)

They read \(\mathrm{2.00x}\) and focus only on the coefficient 2.00, thinking this represents the revenue from each tape dispenser sold rather than recognizing that \(\mathrm{2.00x}\) as a complete expression represents total revenue from all \(\mathrm{x}\) dispensers.

This leads them to select Choice B (The monthly sales revenue, in dollars, from each tape dispenser sold)

Second Most Common Error:

Missing conceptual knowledge: Students don't recognize the profit formula structure, so they guess about what \(\mathrm{2.00x}\) could represent in the business context

Without understanding that \(\mathrm{profit = revenue - costs}\), they might think \(\mathrm{2.00x}\) represents some kind of cost rather than revenue, leading to confusion about whether to choose cost-related options.

This leads to confusion and guessing between Choice C or Choice D

The Bottom Line:

This problem requires recognizing both the mathematical structure of linear equations AND the business context of profit calculations. Students must see that \(\mathrm{2.00x}\) is a complete expression representing total revenue, not just interpret the coefficient 2.00 in isolation.