The cost of 4 notebooks is $20. When 3 notebooks are returned for a refund and 1 pen is purchased,...

1. TRANSLATE the given information

• Given information:
  • 4 notebooks cost \(\$20\)
  • 3 notebooks returned + 1 pen purchased = \(\$7\) net refund
  • Need: cost of 1 notebook + 1 pen

2. INFER the solution strategy

• We need to find individual costs first, then combine them
• Start with notebook cost (straightforward division)
• Use the refund scenario to find pen cost

3. Find the cost of one notebook

Cost per notebook = \(\$20 \div 4 = \$5\)

4. TRANSLATE the refund scenario into math

Refund for 3 notebooks = \(3 \times \$5 = \$15\)

After buying pen: Net refund = \(\$7\)

This means: \(\$15 - \mathrm{pen\ cost} = \$7\)

5. SIMPLIFY to find pen cost

Pen cost = \(\$15 - \$7 = \$8\)

6. Calculate final answer

Total cost = notebook cost + pen cost

Total cost = \(\$5 + \$8 = \$13\)

Answer: C (\(\$13\))

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret "net refund" and think it means the total amount spent rather than the amount received back after all transactions.

They might think: "If net refund is \(\$7\), then the pen must cost \(\$7\)" and calculate \(\$5 + \$7 = \$12\), leading them to guess or select an answer not available in the choices.

Second Most Common Error:

Poor INFER reasoning: Students correctly find that 1 notebook costs \(\$5\), but then get confused about how to use the refund information to find the pen cost.

They might add instead of subtract: \(\$15 + \$7 = \$22\) for pen cost, leading to unrealistic answers and confusion, causing them to abandon systematic solution and guess.

The Bottom Line:

This problem requires understanding that "net refund" represents the final amount received after both returning items (positive cash flow) and purchasing new items (negative cash flow). The key insight is working backwards from this net amount to find the unknown pen cost.