A clothing retailer uses a standard markup strategy for pricing. A store marks up the retail price of a jacket...

1. TRANSLATE the problem information

• Given information:
  • Retail price is 35% greater than wholesale price
  • Wholesale price is p% of retail price
  • Need to find p (rounded to nearest whole number)

• Setting up variables: Let \(\mathrm{W = wholesale\,price, R = retail\,price}\)

2. TRANSLATE each relationship into equations

• "Retail price is 35% greater than wholesale price":
  \(\mathrm{R = W + 35\%\,of\,W = W + 0.35W = 1.35W}\)

• "Wholesale price is p% of retail price":
  \(\mathrm{W = (p/100) \times R}\)

3. INFER the solution strategy

• I need to find p, and I have \(\mathrm{p = (W/R) \times 100}\)
• From my first equation \(\mathrm{R = 1.35W}\), I can find the ratio \(\mathrm{W/R}\)
• Then convert that ratio to a percentage

4. SIMPLIFY to find the ratio W/R

• From \(\mathrm{R = 1.35W}\), divide both sides by 1.35W:
  \(\mathrm{R/(1.35W) = 1}\)
• Rearranging: \(\mathrm{W/R = 1/1.35}\)

5. SIMPLIFY the calculation and apply rounding

• Calculate \(\mathrm{W/R = 1 \div 1.35 = 0.740740...}\) (use calculator)
• Convert to percentage: \(\mathrm{p = 0.740740... \times 100 = 74.074...}\)
• Round to nearest whole number: \(\mathrm{p = 74}\)

Answer: 74

Why Students Usually Falter on This Problem

Most Common Error Path:

Poor TRANSLATE reasoning: Students often confuse the direction of the percentage relationships and write incorrect equations.

For example, they might interpret "retail price is 35% greater than wholesale price" as \(\mathrm{R = 0.35W}\) instead of \(\mathrm{R = 1.35W}\), thinking "35% greater" means "35% of the original" rather than "original plus 35% more." This fundamental misunderstanding leads them to calculate \(\mathrm{p = 285}\) or some other incorrect value, causing confusion and random guessing.

Second Most Common Error:

Weak INFER skill: Students correctly translate both relationships but fail to recognize they need to find the ratio \(\mathrm{W/R}\) to solve for p.

They might try to substitute numbers or get stuck trying to solve the system of equations without recognizing the strategic insight that \(\mathrm{p = (W/R) \times 100}\). This leads to abandoning systematic solution and guessing among reasonable-looking percentages.

The Bottom Line:

This problem requires careful attention to the language of percentage increases and the strategic insight that finding a ratio is the key to solving for the unknown percentage. The most successful students clearly distinguish between "A is 35% greater than B" and "A is 35% of B."