Elena bought 5 lamps that were each the same price. The total cost, including a $20 shipping fee, was $95....

1. TRANSLATE the problem information

• Given information:
  • 5 lamps, each the same price
  • $20 shipping fee (one-time charge)
  • Total cost = $95
  • Find: price of 1 lamp

• What this tells us: The shipping fee is added once to the cost of all 5 lamps

2. TRANSLATE to set up the equation

• Let \(\mathrm{p}\) = price of one lamp
• Cost of 5 lamps: \(\mathrm{5p}\)
• Add one-time shipping: \(\mathrm{5p + 20}\)
• This equals the total: \(\mathrm{5p + 20 = 95}\)

3. SIMPLIFY by solving the equation

• Subtract 20 from both sides:
  \(\mathrm{5p + 20 - 20 = 95 - 20}\)
  \(\mathrm{5p = 75}\)

• Divide both sides by 5:
  \(\mathrm{5p \div 5 = 75 \div 5}\)
  \(\mathrm{p = 15}\)

Answer: A) 15

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misunderstand that the shipping fee applies to the entire order, not per lamp. They might think "each lamp costs some amount, and somehow $20 shipping is involved per lamp" and set up \(\mathrm{5p = 95}\), completely ignoring the shipping fee.

This leads them to solve \(\mathrm{5p = 95}\), getting \(\mathrm{p = 19}\), and select Choice B (19).

Second Most Common Error:

Incomplete SIMPLIFY execution: Students correctly set up \(\mathrm{5p + 20 = 95}\) and correctly subtract to get \(\mathrm{5p = 75}\), but then stop there and think 75 is the answer for one lamp instead of dividing by 5.

This causes them to select Choice D (75).

The Bottom Line:

This problem tests whether students can carefully parse the relationship between individual item costs and additional fees, then follow through with complete algebraic solution. The key insight is recognizing that shipping is a one-time charge applied to the total order, not a per-item cost.