A school administrator plans to purchase the same model of notebook for each of the 75 students. The total budget...

1. TRANSLATE the problem information

• Given information:
  • 75 students each need one notebook
  • Total budget: $17,940
  • This $17,940 is the amount paid AFTER an 8% discount on the list price
• What we need to find: The maximum list price per notebook

2. INFER the discount relationship

• Key insight: If there's an 8% discount, then the amount paid is 92% of the list price
• This means: Amount paid = \(\mathrm{0.92 \times List\ price}\)
• Strategy: Set up an equation where total amount paid equals number of notebooks times discounted price per notebook

3. TRANSLATE this into an equation

• Let \(\mathrm{p}\) = list price per notebook
• Total amount paid = \(\mathrm{75 \times (discounted\ price\ per\ notebook)}\)
• Total amount paid = \(\mathrm{75 \times (0.92p)}\)
• So: \(\mathrm{75 \times 0.92p = 17,940}\)

4. SIMPLIFY to solve for p

• First, multiply: \(\mathrm{75 \times 0.92 = 69}\)
• Now we have: \(\mathrm{69p = 17,940}\)
• Divide both sides by 69: \(\mathrm{p = 17,940 \div 69}\)
• Calculate (use calculator): \(\mathrm{p = 260}\)

Answer: D ($260.00)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret the discount relationship and think the $17,940 IS the list price rather than the discounted price.

They calculate: \(\mathrm{\$17,940 \div 75 = \$239.20}\), then look for the closest answer choice.

This may lead them to select Choice B ($240.00).

Second Most Common Error:

Poor INFER reasoning about discount direction: Students understand there's a discount but get confused about whether to add or subtract the discount from the given amount.

Some students think: "If they got 8% off, the list price must be $17,940 + 8% of $17,940." They calculate \(\mathrm{\$17,940 \times 1.08 = \$19,375.20}\), then divide by 75 to get about $258, leading them to guess among the higher options.

This causes them to get stuck and guess between choices C and D.

The Bottom Line:

The trickiest part is correctly interpreting that the $17,940 is the amount AFTER the discount, not the original list price. Students need to work backwards from the discounted total to find the original per-unit list price.