Maya starts the semester with $24 in her library account credit. Each day she has an overdue book, $4 is...

1. TRANSLATE the problem information

• Given information:
  • Maya starts with \(\$24\) in her account
  • Each day with overdue book: \(\$4\) is deducted
  • Need equation for remaining credit r after d days

2. INFER the mathematical relationship

• Since money is being deducted (taken away), we subtract from the starting amount
• The total deduction depends on number of days: \(\$4 \text{ per day} \times \mathrm{d} \text{ days} = \$4\mathrm{d}\)
• Remaining amount = Starting amount - Total deductions

3. TRANSLATE into equation form

• Starting amount: 24
• Total deductions: 4d
• Remaining credit: \(\mathrm{r} = 24 - 4\mathrm{d}\)

Answer: C

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret "deducted" and think the \(\$4\) should be added rather than subtracted, or they confuse which quantity should be multiplied by d.

Some students see "24" and "4" with "d" and think about multiplying 24 by something, leading them toward expressions like \(24(\mathrm{d} + 4)\). This may lead them to select Choice B : r = 24(d + 4) .

Second Most Common Error:

Poor TRANSLATE reasoning: Students correctly identify subtraction is needed but get the order wrong, thinking the deductions come first.

They might reason "4 times d days, then subtract the starting 24" instead of "starting 24, then subtract 4 times d days." This may lead them to select Choice D (\(\mathrm{r} = 4\mathrm{d} - 24\)).

The Bottom Line:

This problem tests whether students can correctly translate a decrease scenario into mathematical notation. The key insight is recognizing that "deducted from" means we subtract the variable amount from the fixed starting amount.