At the start of a highway trip, a car's fuel tank contains 12 gallons of gasoline. The function \(\mathrm{F(d) =...

1. TRANSLATE the function components

• Given: \(\mathrm{F(d) = 12 - 0.05d}\) represents gallons remaining after d miles
• What this tells us:
  • \(\mathrm{12}\) = starting fuel amount (gallons)
  • \(\mathrm{0.05d}\) = fuel consumed after traveling d miles
  • Therefore: \(\mathrm{0.05}\) = gallons consumed per mile

2. INFER the relationship to fuel efficiency

• The question asks for fuel efficiency in miles per gallon
• We found the car consumes \(\mathrm{0.05}\) gallons per mile
• Fuel efficiency is the reciprocal: miles per gallon = \(\mathrm{1 ÷ (gallons\ per\ mile)}\)

3. SIMPLIFY to find the final answer

• Miles per gallon = \(\mathrm{1 ÷ 0.05 = 20}\)

Answer: C (20)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students don't recognize that fuel efficiency is the reciprocal of the consumption rate. They might think the coefficient \(\mathrm{0.05}\) directly represents fuel efficiency, or they focus on the \(\mathrm{12}\) gallons as somehow being the efficiency measure.

This may lead them to select Choice B (12) by incorrectly thinking the initial fuel amount represents efficiency.

Second Most Common Error:

Poor TRANSLATE reasoning: Students misinterpret what the coefficient \(\mathrm{-0.05}\) represents in the context. They might see it as a decreasing rate but fail to understand it represents gallons consumed per mile.

This leads to confusion about what calculation to perform and causes them to get stuck and guess.

The Bottom Line:

This problem requires students to move beyond just reading the function to understanding what the rate coefficient means in real-world context, then applying the reciprocal relationship between inverse rate units.