A librarian has 43 books to distribute to a group of children. If he gives each child 2 books, he...

1. TRANSLATE the problem information

• Given information:
  • Total books: 43
  • Books per child: 2
  • Books left over: 7
  • Unknown: number of children

2. INFER the mathematical relationship

• Key insight: The total books equals distributed books plus leftover books
• If \(\mathrm{n = number\,of\,children}\), then \(\mathrm{distributed\,books = 2n}\)
• This gives us: \(\mathrm{2n + 7 = 43}\)

3. SIMPLIFY to solve for the number of children

• Subtract 7 from both sides: \(\mathrm{2n = 43 - 7 = 36}\)
• Divide by 2: \(\mathrm{n = 36 ÷ 2 = 18}\)

Answer: B. 18

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misunderstand how to handle the remainder and incorrectly divide the total by books per child first.

They think: "43 books ÷ 2 books per child = 21.5, so about 22 children, then subtract the 7 leftover books to get \(\mathrm{22 - 7 = 15}\)."

This may lead them to select Choice A (15).

Second Most Common Error:

Poor TRANSLATE reasoning: Students incorrectly add the leftover books to the total before dividing.

They think: "If there are 7 books left over, maybe I need \(\mathrm{43 + 7 = 50}\) total books, then \(\mathrm{50 ÷ 2 = 25}\) children."

This may lead them to select Choice C (25).

The Bottom Line:

The key challenge is correctly interpreting that the 7 leftover books are already included in the 43 total books, not additional to them. Students must recognize that "total = distributed + leftover" rather than trying to work directly with the total.