Question:A store owner increases the price of an item from $40 to $50. The increase in price is what percentage...

1. TRANSLATE the problem information

• Given information:
  • Original price: \(\$40\)
  • New price: \(\$50\)
• What we need to find: The increase as a percentage of the original price

2. INFER what calculation is needed first

• We need the actual dollar amount of the increase
• Price increase = New price - Original price = \(\$50 - \$40 = \$10\)

3. TRANSLATE the key phrase into math

• "What percentage of the original price" means:
  • The increase (\(\$10\)) is the "part"
  • The original price (\(\$40\)) is the "whole"
• This gives us the setup: \(\frac{\mathrm{Increase}}{\mathrm{Original\ Price}} \times 100\%\)

4. SIMPLIFY the calculation

• Substitute values: \(\frac{\$10}{\$40} \times 100\%\)
• Simplify the fraction: \(\frac{\$10}{\$40} = \frac{1}{4}\)
• Convert to percentage: \(\frac{1}{4} \times 100\% = 25\%\)

Answer: (C) 25%

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students misinterpret "percentage of the original price" and use the new price (\(\$50\)) as the denominator instead of the original price (\(\$40\)).

Their calculation becomes: \(\frac{\$10}{\$50} \times 100\% = 20\%\)

This leads them to select Choice (B) (20%)

Second Most Common Error:

Poor TRANSLATE reasoning: Students calculate the new price as a percentage of the original price instead of just the increase.

They compute: \(\frac{\$50}{\$40} \times 100\% = 125\%\), then get confused about what this means in the context of the answer choices. This leads to confusion and guessing.

The Bottom Line:

The critical insight is recognizing that "percentage of the original price" specifically refers to using the original price as the base (denominator) for the percentage calculation, not the new price.