In March, the price of a collectible card was $15.50. In April, the price of the collectible card was $17.36....

1. TRANSLATE the problem information

• Given information:
  • March price: \(\$15.50\)
  • April price: \(\$17.36\)
  • April price was p% of March price

• What this tells us: We need to find what percent the April price represents relative to the March price

2. TRANSLATE the percentage relationship into an equation

• "April price was p% of March price" means:
  \(\$17.36 = (\mathrm{p}/100) \times \$15.50\)

• This is our key equation to solve

3. SIMPLIFY by solving the equation

• Start with: \(17.36 = (\mathrm{p}/100) \times 15.50\)
• Rewrite as: \(17.36 = 15.50\mathrm{p}/100\)
• Multiply both sides by 100: \(1736 = 15.50\mathrm{p}\)
• Divide both sides by 15.50: \(\mathrm{p} = 1736 \div 15.50\) (use calculator)
• Calculate: \(\mathrm{p} = 112\)

Answer: 112

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students confuse "percent of" with "percent increase" and calculate how much the price increased instead of the percentage relationship.

They calculate: \((17.36 - 15.50)/15.50 \times 100 = 1.86/15.50 \times 100 = 12\%\)

This leads them to select Choice A (12).

Second Most Common Error:

Poor TRANSLATE reasoning: Students set up the equation backwards, thinking the March price is p% of the April price instead of the other way around.

They write: \(15.50 = (\mathrm{p}/100) \times 17.36\), leading to \(\mathrm{p} \approx 89.3\), causing confusion and potentially guessing among the remaining choices.

The Bottom Line:

The key challenge is correctly interpreting "April price was p% of March price" - this means April = p% × March, not that p represents the change between the prices. When April is greater than March, p will be greater than 100%.