Question:A wholesaler runs a promotion in which each paid unit includes 4 additional units for free. A retailer ends up...

1. TRANSLATE the promotion details

• Given information:
  • Each paid unit includes 4 additional free units
  • Total units received: 60
  • Find: number of units paid for

• What this tells us: For every 1 unit you pay for, you receive \(1 + 4 = 5\) total units

2. INFER the mathematical relationship

• Let \(\mathrm{p}\) = number of units paid for
• Since each paid unit gives you 5 total units: \(5\mathrm{p}\) = total units received
• We know total units = 60, so: \(5\mathrm{p} = 60\)

3. SIMPLIFY to find the answer

• Divide both sides by 5: \(\mathrm{p} = 60 \div 5 = 12\)
• Check our work: \(12 \times 5 = 60\) total units ✓

Answer: B (12)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret "each paid unit includes 4 additional units for free" and think you get 4 total units per paid unit instead of 5 total units (1 paid + 4 free).

Using this incorrect interpretation: \(4\mathrm{p} = 60\), so \(\mathrm{p} = 15\)

This leads them to select Choice C (15).

Second Most Common Error:

Poor INFER reasoning: Students set up the wrong equation by thinking about the free units separately. They might reason: "paid units + free units = 60" and since free units = 4 × paid units, they get \(\mathrm{p} + 4\mathrm{p} = 60\), leading to \(5\mathrm{p} = 60\). While this actually gives the correct answer, the reasoning path shows confusion about the problem structure.

The Bottom Line:

This problem tests your ability to carefully parse promotional language and translate it into clear mathematical relationships. The key insight is recognizing that "each paid unit includes 4 additional free units" means each paid unit results in 5 total units, not 4.