Maya spent $58 at a comic book convention buying graphic novels and collectible bookmarks. Each graphic novel cost $4, and...

1. TRANSLATE the problem information

• Given information:
  • Total spent: \(\$58\)
  • Cost per graphic novel: \(\$4\)
  • Cost per bookmark: \(\$2\)
  • Number of graphic novels bought: \(9\)
• What we need to find: Number of bookmarks bought

2. INFER the solution approach

• Since we know the total spent and have mixed items at different prices, we need to:
  • Find the cost of one type of item first (graphic novels)
  • Subtract to isolate the cost of the other type (bookmarks)
  • Divide by unit cost to find quantity

3. Calculate the cost of graphic novels

• \(9\) graphic novels \(\times\) \(\$4\) each \(= \$36\)

4. SIMPLIFY to find bookmark spending

• Amount spent on bookmarks = Total spending - Graphic novel spending
• \(\$58 - \$36 = \$22\)

5. SIMPLIFY to find number of bookmarks

• Number of bookmarks = Bookmark spending ÷ Cost per bookmark
• \(\$22 \div \$2 = 11\) bookmarks

Answer: 11 bookmarks (Choice B)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misread the problem and try to divide the total \(\$58\) by something, missing that they need to separate the costs of different items first.

They might calculate \(\$58 \div \$2 = 29\) and select Choice E (29), thinking this gives them the total number of bookmarks without accounting for the graphic novels already purchased.

Second Most Common Error:

Poor INFER reasoning: Students correctly find that graphic novels cost \(\$36\), but then make a strategic error in the next step.

Instead of subtracting to isolate bookmark costs, they might add: \(\$36 + \$2 = \$38\), then try to work with this meaningless number. This leads to confusion and guessing among the remaining choices.

The Bottom Line:

This problem requires students to work systematically through a multi-step cost breakdown. The key insight is recognizing that when you have mixed purchases at different unit prices, you must isolate the spending on each type before finding quantities.