A lab notebook has room for 24 data entries on the first page because of a title block. Each additional...

1. TRANSLATE the problem information

• Given information:
  • First page: 24 entries (due to title block)
  • Each additional page: 28 entries
  • Total pages used: x
  • Need equation for total entries y

2. INFER the mathematical structure

• Key insight: The first page is different from all other pages
• For x total pages, we have:
  • 1 first page with 24 entries
  • (x-1) additional pages with 28 entries each
• Total entries = entries on first page + entries on additional pages

3. TRANSLATE this structure into an equation

• \(\mathrm{y = 24 + 28(x - 1)}\)

4. SIMPLIFY the equation algebraically

• \(\mathrm{y = 24 + 28(x - 1)}\)
• \(\mathrm{y = 24 + 28x - 28}\)
• \(\mathrm{y = 28x - 4}\)

5. Verify with test values

• Test \(\mathrm{x = 1}\): \(\mathrm{y = 28(1) - 4 = 24}\) ✓ (only first page)
• Test \(\mathrm{x = 2}\): \(\mathrm{y = 28(2) - 4 = 52}\) ✓ (first page + one additional: \(\mathrm{24 + 28 = 52}\))

Answer: D

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret "additional pages" and think all x pages hold 28 entries, leading to \(\mathrm{y = 28x}\).
This may lead them to select Choice B (\(\mathrm{y = 28x}\)).

Second Most Common Error:

Poor INFER reasoning: Students recognize the first page is special but incorrectly think the total should be \(\mathrm{28x + 24}\) (adding the extra capacity rather than accounting for the reduced first page capacity).
This may lead them to select Choice C (\(\mathrm{y = 28x + 24}\)).

The Bottom Line:

This problem tests whether students can handle situations where the first term in a pattern is different from the rest—a common real-world scenario that requires careful setup of the mathematical model.