A manufacturing company produces electronic components at a cost of $12.00 per unit. Due to increased market demand, the company...

1. TRANSLATE the problem information

• Given information:
  • Production cost = \(\$12.00\) per unit
  • Selling price = \(150\%\) of production cost
  • Discount = \(60\%\) off the selling price
• What we need to find: Final discounted price per unit

2. TRANSLATE the first calculation

• "\(150\%\) of production cost" means: \(1.50 \times \$12.00 = \$18.00\)
• So the selling price is \(\$18.00\)

3. INFER the discount strategy

• "\(60\%\) off the selling price" means we need to:
  • Either calculate \(60\%\) of \(\$18.00\) and subtract it, OR
  • Calculate \(40\%\) of \(\$18.00\) directly (since paying \(40\%\) is the same as getting \(60\%\) off)

4. SIMPLIFY using the subtraction approach

• Discount amount = \(60\%\) of \(\$18.00\) = \(0.60 \times \$18.00 = \$10.80\)
• Final price = \(\$18.00 - \$10.80 = \$7.20\)

5. SIMPLIFY verification using direct approach

• Final price = \(40\%\) of \(\$18.00\) = \(0.40 \times \$18.00 = \$7.20\) ✓

Answer: B) \(\$7.20\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Applying the discount percentage to the wrong base amount

Students might think "\(60\%\) discount" applies to the original production cost rather than the selling price. This leads them to calculate: Final price = \(\$18.00 - (0.60 \times \$12.00) = \$18.00 - \$7.20 = \$10.80\)

This may lead them to select Choice C (\(\$10.80\))

Second Most Common Error:

Poor SIMPLIFY execution: Reporting an intermediate calculation as the final answer

Students correctly calculate the discount amount (\(\$10.80\)) but then report this as their final answer instead of subtracting it from the selling price. They might also just report the selling price (\(\$18.00\)) or production cost (\(\$12.00\)) if they get confused about what the question is asking for.

This may lead them to select Choice C (\(\$10.80\)), Choice D (\(\$12.00\)), or Choice E (\(\$18.00\))

The Bottom Line:

This problem tests whether students can carefully track what percentage applies to which amount in a multi-step pricing scenario. The key insight is that discounts apply to selling prices, not production costs.