Cathy has n CDs. Gerry has 3 more than twice the number of CDs that Cathy has. In terms of...

1. TRANSLATE the problem information

• Given information:
  • Cathy has \(\mathrm{n}\) CDs
  • Gerry has 3 more than twice the number of CDs that Cathy has
• We need to find Gerry's number of CDs in terms of \(\mathrm{n}\)

2. TRANSLATE the key phrase step by step

• Break down "3 more than twice the number of CDs that Cathy has":
  • "the number of CDs that Cathy has" = \(\mathrm{n}\)
  • "twice the number of CDs that Cathy has" = \(\mathrm{2n}\)
  • "3 more than twice the number of CDs that Cathy has" = \(\mathrm{2n + 3}\)

3. INFER the final answer

• Since Gerry has \(\mathrm{2n + 3}\) CDs, we can match this to the answer choices
• Looking at the options, this corresponds to choice D

Answer: D. \(\mathrm{2n + 3}\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misread "3 more than twice" as "three times"

They incorrectly think the phrase means "three times the number of CDs" instead of "twice the number plus 3." This leads them to write \(\mathrm{3n}\) instead of \(\mathrm{2n + 3}\).

This may lead them to select Choice A (\(\mathrm{3n - 2}\)) or Choice B (\(\mathrm{3n + 2}\))

Second Most Common Error:

Poor TRANSLATE reasoning: Students confuse "more than" with "less than"

They correctly identify "twice the number" as \(\mathrm{2n}\) but then subtract 3 instead of adding 3, thinking "3 more than" somehow means subtract.

This may lead them to select Choice C (\(\mathrm{2n - 3}\))

The Bottom Line:

Success on this problem depends entirely on careful translation of English to mathematical symbols. Students need to break down complex phrases word by word and understand that "more than" always means addition, while "twice" always means multiply by 2.