d = 16 - x/30. The equation shown gives the estimated amount of diesel d, in gallons, that remains in...

1. TRANSLATE the problem information

• Given information:
  • Equation: \(\mathrm{d = 16 - \frac{x}{30}}\)
  • \(\mathrm{d}\) = gallons of diesel remaining
  • \(\mathrm{x}\) = miles driven
  • Need to find \(\mathrm{d}\) when \(\mathrm{x = 300}\)

• What this tells us: We need to substitute \(\mathrm{x = 300}\) into the equation and solve for \(\mathrm{d}\).

2. SIMPLIFY by substituting and calculating

• Substitute \(\mathrm{x = 300}\) into \(\mathrm{d = 16 - \frac{x}{30}}\):

\(\mathrm{d = 16 - \frac{300}{30}}\)

• Calculate the division first (order of operations):

\(\mathrm{300 \div 30 = 10}\)

• Complete the subtraction:

\(\mathrm{d = 16 - 10 = 6}\)

Answer: B (6 gallons)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Students make arithmetic errors, particularly with the division \(\mathrm{\frac{300}{30}}\), calculating it as something other than 10. For example, they might calculate \(\mathrm{\frac{300}{30}}\) as 100 or struggle with the division entirely.

This may lead them to select an incorrect choice or abandon the problem due to calculation confusion.

Second Most Common Error:

Poor TRANSLATE reasoning: Students might misread the problem and substitute the wrong value for \(\mathrm{x}\), such as confusing other numbers mentioned in the problem or using one of the boundary values (0 or 480) instead of the specified \(\mathrm{x = 300}\).

Looking at the answer choices, this could lead them to select Choice A (0) if they use \(\mathrm{x = 480}\), Choice C (14) if they use \(\mathrm{x = 60}\), or Choice D (16) if they use \(\mathrm{x = 0}\).

The Bottom Line:

This problem tests whether students can systematically substitute a value into a linear equation and perform accurate arithmetic. The key is careful reading and methodical calculation.