A laptop is on sale for 20% off its original price. The sale price is p times the original price....

1. TRANSLATE the problem information

• Given information:
  • Laptop is on sale for 20% off its original price
  • The sale price is p times the original price
  • We need to find the value of p

• What this tells us: We need to express the sale price in terms of the original price and find what multiplier p represents.

2. INFER the relationship between discount and final price

• Key insight: "20% off" doesn't mean \(\mathrm{p = 0.2}\)
• When something is 20% off, you pay 80% of the original price
• So we need to find what fraction of the original price you actually pay

3. Set up the mathematical relationship

Let the original price = O

• Discount amount = 20% of O = \(\mathrm{0.20 \times O}\)
• Sale price = Original price - Discount = \(\mathrm{O - 0.20O}\)

4. SIMPLIFY the sale price expression

• Sale price = \(\mathrm{O - 0.20O}\)
  = \(\mathrm{O(1 - 0.20)}\)
  = \(\mathrm{0.80O}\)

5. TRANSLATE the second condition and solve

• The problem states: sale price = \(\mathrm{p \times \text{original price}}\)
• So: \(\mathrm{0.80O = p \times O}\)
• SIMPLIFY by dividing both sides by O: \(\mathrm{p = 0.80 = 0.8}\)

Answer: (B) 0.8

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students confuse the discount rate with the multiplier p.

They see "20% off" and immediately think \(\mathrm{p = 0.2}\), forgetting that p represents what fraction of the original price you actually pay, not the discount amount.

This leads them to select Choice (A) (0.2).

Second Most Common Error:

Poor INFER reasoning: Students incorrectly add the discount percentage instead of subtracting it.

They might think: "If it's 20% off, then the sale price is 120% of some base price," leading them to calculate \(\mathrm{p = 1.2}\).

This causes them to select Choice (C) (1.2).

The Bottom Line:

The key insight is understanding what p represents. It's not the discount rate—it's the fraction of the original price that you actually pay after the discount is applied.