What percentage of 300 is 75?

1. TRANSLATE the problem information

• Given information:
  • We need to find what percentage of 300 equals 75
  • Let x represent the unknown percentage

• This translates to the equation: \(\mathrm{x\%\ of\ 300 = 75}\)

2. TRANSLATE percentage notation to algebraic form

• Convert x% to decimal form: \(\mathrm{x\% = \frac{x}{100}}\)
• The equation becomes: \(\mathrm{\frac{x}{100} \times 300 = 75}\)

3. SIMPLIFY the equation through algebraic steps

• Multiply the left side: \(\mathrm{\frac{x}{100} \times 300 = 3x}\)
• Our equation is now: \(\mathrm{3x = 75}\)
• Divide both sides by 3: \(\mathrm{x = 25}\)

4. Verify the answer

• Check: \(\mathrm{25\%\ of\ 300 = 0.25 \times 300 = 75}\) ✓

Answer: A. 25%

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students may confuse which number represents the "whole" and which represents the "part" in percentage problems. They might set up the equation backwards or mix up the given values.

For example, they might think "75% of what number is 300?" instead of "what percentage of 300 is 75?" This confusion in the setup leads to completely different equations and wrong answers. This may lead them to select Choice C (75%) by mistakenly thinking the given number 75 is the percentage.

Second Most Common Error:

Poor SIMPLIFY execution: Students correctly set up \(\mathrm{\frac{x}{100} \times 300 = 75}\) but make computational errors when simplifying. They might incorrectly calculate \(\mathrm{\frac{x}{100} \times 300}\) as something other than 3x, or make division errors when solving \(\mathrm{3x = 75}\).

These calculation mistakes can lead to values like 50 or other incorrect percentages. This may lead them to select Choice B (50%) or guess among the remaining options.

The Bottom Line:

Percentage problems require careful translation of the English phrase into mathematical notation, paying close attention to which quantity represents the whole (300) and which represents the part (75). The key insight is recognizing that "what percentage of A is B" always translates to \(\mathrm{\frac{x}{100} \times A = B}\).