A copier produces pages at a constant rate of 24 pages per minute. During a print job, the copier produces...

1. TRANSLATE the problem information

• Given information:
  • Copier rate: 24 pages per minute
  • Total pages produced: 168 pages
  • Find: number of minutes the copier ran

• What this tells us: We have a rate situation where \(\mathrm{rate \times time = total\ amount}\)

2. TRANSLATE to set up the equation

• Since \(\mathrm{rate \times time = total\ amount}\):
• \(\mathrm{24\ pages/minute \times time = 168\ pages}\)
• This gives us: \(\mathrm{24t = 168}\)

3. SIMPLIFY to solve for time

• Divide both sides by 24:
• \(\mathrm{t = 168 \div 24}\)
• \(\mathrm{t = 7}\) (use calculator)

Answer: B. 7

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students see the number 24 and think it might be the answer, especially since it appears as choice D. They don't set up the rate equation properly and just select the given rate as their answer.

This may lead them to select Choice D (24).

Second Most Common Error:

Poor SIMPLIFY execution: Students correctly set up 168 ÷ 24 but make arithmetic errors in the division, perhaps getting confused with the calculation or making a computational mistake.

This may lead them to select Choice A (6) or cause them to get stuck and guess.

The Bottom Line:

This problem tests whether students can recognize a rate situation and apply the fundamental relationship that rate × time = total amount. The key is translating the words into the correct mathematical setup rather than just picking numbers that appear in the problem.