A bakery owner made a profit of $139 on custom cakes after deducting a fixed overhead cost of $29 and...

1. TRANSLATE the problem information

• Given information:
  • Profit made: $139
  • Fixed overhead cost: $29 (this gets deducted)
  • Revenue: \(\mathrm{p}\) cakes sold at $12 each = \(\mathrm{12p}\) dollars

2. INFER the relationship between profit, revenue, and costs

• The key insight: \(\mathrm{Profit = Revenue - Costs}\)
• Revenue comes from selling cakes: \(\mathrm{12p}\)
• The overhead cost of $29 is subtracted from revenue
• So: \(\mathrm{Profit = 12p - 29}\)

3. Set up the equation

• We know the profit is $139
• Therefore: \(\mathrm{12p - 29 = 139}\)

Answer: A

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret "after deducting a fixed overhead cost" and think this means the cost gets added to the profit rather than subtracted from the revenue.

Their reasoning: "The profit is $139 and there's also a $29 cost, so the total is \(\mathrm{12p = 139 + 29}\)."

This may lead them to select Choice C (\(\mathrm{12p + 29 = 139}\)).

Second Most Common Error:

Poor TRANSLATE reasoning: Students mix up which numbers represent the price per cake versus the overhead cost, thinking the $29 is the price per cake and $12 is the overhead.

This confusion about which number goes where leads them to set up equations like \(\mathrm{29p - 12 = 139}\).

This may lead them to select Choice B (\(\mathrm{29p - 12 = 139}\)) or Choice D (\(\mathrm{29p + 12 = 139}\)).

The Bottom Line:

This problem tests whether students can correctly translate a business scenario into algebra while keeping track of what each number represents and understanding that profit means "what's left after subtracting costs."