A publisher's total budget for printing a batch of books is $2,800. The total cost depends on the number of...

1. TRANSLATE the equation structure

• Given equation: \(2800 - 0.04\mathrm{B} = 0.24\mathrm{C}\)
• This represents: Total budget - (cost of B&W pages) = (cost of color pages)
• Key insight: The coefficients tell us the cost per page:
  • \(0.04\mathrm{B}\) means each black-and-white page costs \(\$0.04\)
  • \(0.24\mathrm{C}\) means each color page costs \(\$0.24\)

2. INFER what the question is asking

• We need the difference in cost per page, expressed in cents
• Strategy: Find unit costs, convert to cents, then subtract

3. SIMPLIFY through unit conversion and calculation

• Convert dollar costs to cents:
  • Black-and-white: \(\$0.04 \times 100 = 4\) cents per page
  • Color: \(\$0.24 \times 100 = 24\) cents per page
• Calculate difference: \(24 - 4 = 20\) cents

Answer: C) 20

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students see the equation but don't recognize that the coefficients (0.04 and 0.24) represent the cost per individual page. They might try to manipulate the equation algebraically instead of interpreting what the numbers mean in context.

This leads to confusion and guessing, as they can't connect the equation structure to the real-world costs.

Second Most Common Error:

Poor SIMPLIFY execution: Students correctly identify the unit costs as \(\$0.04\) and \(\$0.24\) but forget to convert to cents, giving their answer as 0.2 dollars instead of 20 cents.

This may lead them to select Choice A (0.2).

The Bottom Line:

This problem tests whether students can interpret the meaning of coefficients in a cost equation, not just manipulate the algebra. The key insight is recognizing that in a term like \(0.04\mathrm{B}\), the 0.04 tells us the cost per individual unit.