During a sale, the original prices of all the items in a clothing store have been reduced by 20%. What...

1. TRANSLATE the problem information

• Given information:
  • Original price of jacket: \(\$50\)
  • All items reduced by \(20\%\)
  • Need to find: sale price

• What "reduced by \(20\%\)" means: Take away \(20\%\) of the original price from the original price

2. INFER the solution approach

• To find sale price, we need to:
  1. Calculate how much money is taken off (the discount amount)
  2. Subtract that discount from the original price

• We'll use: Sale Price = Original Price - Discount Amount

3. SIMPLIFY to find the discount amount

• Discount amount = \(20\%\) of \(\$50\)
• \(20\% = 0.20\), so: \(0.20 \times \$50 = \$10\)

4. SIMPLIFY to find the sale price

• Sale price = Original price - Discount amount
• Sale price = \(\$50 - \$10 = \$40\)

Answer: D. \(\$40\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Conceptual confusion about "reduced by" vs "reduced to": Students may misinterpret "reduced by \(20\%\)" as meaning "the new price is \(20\%\) of the original price" rather than "\(20\%\) is taken away from the original price."

This leads them to calculate: \(\$50 \times 0.20 = \$10\), making them select Choice A (\(\$12\)) or get confused about why \(\$10\) isn't an option.

Second Most Common Error:

Weak SIMPLIFY execution: Students correctly understand the concept but make arithmetic errors when calculating \(20\%\) of \(\$50\), perhaps getting \(\$5\) instead of \(\$10\), or incorrectly adding the discount instead of subtracting it.

This may lead them to select Choice B (\(\$30\)) (if they subtracted incorrectly calculated \(20\% = \$20\)) or other incorrect choices.

The Bottom Line:

The key challenge is translating everyday discount language into precise mathematical operations. Students must clearly distinguish between "reduced by X%" (subtract X% from 100%) and "reduced to X%" (the final price is X% of original).