A store sells two different-sized containers of a certain Greek yogurt. The store's sales of this Greek yogurt totaled 1,277.94...

1. TRANSLATE the problem information

• Given information:
  • Store sells two sizes of Greek yogurt containers
  • Total sales last month: \(\$1,277.94\)
  • Equation: \(5.48\mathrm{x} + 7.30\mathrm{y} = 1,277.94\)
  • \(\mathrm{x}\) = number of smaller containers sold
  • \(\mathrm{y}\) = number of larger containers sold
• What this tells us: This equation represents the total revenue as the sum of revenue from each container type

2. INFER what each part of the equation means

• In revenue equations, we typically have: \((\mathrm{price\ per\ unit}) \times (\mathrm{number\ of\ units}) = \mathrm{total\ revenue}\)
• Looking at \(5.48\mathrm{x}\): This must be \((\mathrm{price\ per\ small\ container}) \times (\mathrm{number\ of\ small\ containers})\)
• Looking at \(7.30\mathrm{y}\): This must be \((\mathrm{price\ per\ large\ container}) \times (\mathrm{number\ of\ large\ containers})\)
• The question asks for the price of each smaller container

3. INFER the final answer

• Since \(5.48\mathrm{x} = (\mathrm{price\ per\ small\ container}) \times \mathrm{x}\)
• The coefficient \(5.48\) must be the price per smaller container
• We can verify: \(7.30\) would be the price per larger container

Answer: A. 5.48

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misunderstand what \(5.48\mathrm{x}\) represents versus what \(5.48\) represents.

They see \(5.48\mathrm{x}\) in the equation and think "this whole expression must be the price per container" rather than recognizing that \(5.48\mathrm{x}\) represents total revenue from small containers while \(5.48\) alone represents the unit price.

This may lead them to select Choice D (\(5.48\mathrm{x}\)).

Second Most Common Error:

Poor TRANSLATE reasoning: Students correctly identify that we need a unit price, but misread which variable corresponds to which container size.

They might think \(\mathrm{y}\) represents smaller containers instead of \(\mathrm{x}\), leading them to identify \(7.30\) as the price per smaller container.

This may lead them to select Choice C (\(7.30\)).

The Bottom Line:

Success requires carefully translating the equation structure to understand that coefficients represent unit prices while the full terms (like \(5.48\mathrm{x}\)) represent total revenues for each product type.