A store sells two different-sized containers of blueberries. The store's sales of these blueberries totaled 896.86 dollars last month. The...

1. TRANSLATE the equation components

• Given information:
  • Equation: \(4.51\mathrm{x} + 6.07\mathrm{y} = 896.86\)
  • \(\mathrm{x}\) = number of smaller containers sold
  • \(\mathrm{y}\) = number of larger containers sold
  • \(896.86\) = total sales in dollars
• What this tells us: This is a revenue equation where each term represents sales from one container type

2. INFER the meaning of each term

• In revenue problems, we use the pattern: (price per item) × (quantity) = total revenue for that item
• Since \(4.51\mathrm{x}\) represents total sales from small containers, and \(\mathrm{x}\) is the quantity of small containers:
  • \(4.51\) must be the price per small container
  • Similarly, \(6.07\) must be the price per large container

3. APPLY CONSTRAINTS to answer the specific question

• The question asks specifically for the price of each smaller container
• From our analysis: price per small container = \(4.51\)

Answer: $4.51

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students may confuse which coefficient goes with which container size, especially if they misread the variable definitions. They might think \(\mathrm{y}\) represents small containers instead of \(\mathrm{x}\), leading them to incorrectly identify \(6.07\) as the price of small containers.

This confusion about variable meanings can cause them to select the wrong coefficient and arrive at $6.07 instead of $4.51.

The Bottom Line:

Success on this problem depends entirely on carefully reading the variable definitions and understanding that in multiplication, when one factor represents quantity, the other factor represents the rate or price per unit.