A distribution center processes two types of orders: standard and express. On a particular day, the center processed 180 standard...

1. TRANSLATE the equation components

• Given equation: \(\mathrm{180s + 60e = 4,320}\)
• Context: 180 standard orders, 60 express orders, total cost $4,320
• What this tells us: Each term represents a portion of the total cost

2. INFER the meaning of each term

• The equation follows the pattern: \(\mathrm{(quantity_1 \times unit\ cost_1) + (quantity_2 \times unit\ cost_2) = total\ cost}\)
• \(\mathrm{180s}\) means: 180 standard orders × s dollars per standard order
• \(\mathrm{60e}\) means: 60 express orders × e dollars per express order

3. INFER what the variable e represents

• Since \(\mathrm{60e}\) = total cost for express orders
• And there are 60 express orders
• Then \(\mathrm{e}\) = cost per express order
• This is the average shipping cost for one express order

Answer: A) The average shipping cost, in dollars, for an express order.

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students focus on what the entire term \(\mathrm{60e}\) represents instead of what the variable \(\mathrm{e}\) alone represents.

They correctly identify that \(\mathrm{60e}\) represents the total cost for express orders, but then mistakenly think that \(\mathrm{e}\) also represents a total cost. This confusion between the term (\(\mathrm{60e}\)) and the variable (\(\mathrm{e}\)) leads them to select Choice C (The total shipping cost, in dollars, for all express orders).

Second Most Common Error:

Poor TRANSLATE reasoning: Students misinterpret which coefficient goes with which type of order.

They might think that since 180 is larger than 60, the variable \(\mathrm{s}\) must go with standard orders and \(\mathrm{e}\) with express orders, but then confuse themselves about whether the variables represent per-unit costs or total costs. This leads to guessing between choices or selecting Choice B if they swap the variables.

The Bottom Line:

This problem tests whether students understand the fundamental structure of linear cost equations: \(\mathrm{coefficient \times variable = quantity \times unit\ cost}\). The key insight is recognizing that variables typically represent unit amounts, not totals, when multiplied by known quantities.