A 3D printer uses 12 grams of filament for each minute it prints. Before printing begins, the machine uses an...

1. TRANSLATE the problem information

• Given information:
  • 12 grams of filament used per minute of printing
  • 18 grams of filament used once for priming (before printing starts)
  • \(\mathrm{x}\) = printing time in minutes
  • \(\mathrm{g}\) = total grams of filament needed

2. INFER the cost structure

• This is a linear cost problem with two parts:
  • Fixed cost: 18 grams (happens once, regardless of printing time)
  • Variable cost: 12 grams per minute × number of minutes
• The total will be: Fixed cost + Variable cost

3. TRANSLATE each cost component into algebra

• Fixed cost = 18 grams
• Variable cost = 12 grams/minute × \(\mathrm{x}\) minutes = \(\mathrm{12x}\) grams
• Total cost: \(\mathrm{g = 18 + 12x = 12x + 18}\)

4. Verify by testing with sample values

• If \(\mathrm{x = 2}\) minutes:
  \(\mathrm{g = 12(2) + 18}\)
  \(\mathrm{g = 24 + 18}\)
  \(\mathrm{g = 42\ grams}\)
• This makes sense: 18 for priming + 24 for 2 minutes of printing

Answer: C

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students mix up which number goes with which operation, creating \(\mathrm{g = 18x + 12}\) instead of \(\mathrm{g = 12x + 18}\).

They incorrectly think "18 grams per minute" and "12 grams fixed," when the problem clearly states 12 grams per minute and 18 grams for priming. This happens when students don't carefully track which number corresponds to which part of the problem.

This leads them to select Choice B (\(\mathrm{g = 18x + 12}\)).

Second Most Common Error:

Incomplete TRANSLATE reasoning: Students only account for the printing time and ignore the priming cost entirely.

They see "12 grams per minute for x minutes" and create \(\mathrm{g = 12x}\), completely missing that there's also a one-time 18-gram cost before printing begins. This happens when students don't read through the entire problem before setting up their equation.

This leads them to select Choice A (\(\mathrm{g = 12x}\)).

The Bottom Line:

This problem tests whether students can distinguish between fixed costs (happen once) and variable costs (depend on time or quantity) when building linear equations from real-world situations.