The boiling point of water at sea level is 212 degrees Fahrenheit (°F). For every 550 feet above sea level,...

1. TRANSLATE the given information

• Given information:
  • Base condition: Boiling point at sea level = \(212°\mathrm{F}\)
  • Rate of change: Every \(550\) feet up → temperature drops \(1°\mathrm{F}\)
  • Variable: \(\mathrm{x}\) feet above sea level
  • Find: Equation for boiling point B

• What this tells us: We have a starting value (\(212°\mathrm{F}\)) that decreases at a constant rate as altitude increases.

2. INFER how the rate applies to any height

• At \(\mathrm{x}\) feet above sea level, we need to calculate how many 550-foot increments that represents
• Number of increments = \(\mathrm{x} ÷ 550 = \frac{\mathrm{x}}{550}\)
• Each increment reduces temperature by \(1°\mathrm{F}\)
• Total temperature reduction = \(\frac{\mathrm{x}}{550} × 1°\mathrm{F} = \frac{\mathrm{x}}{550}\) degrees

3. TRANSLATE "lowered by" into mathematical operation

• "Lowered by" means we subtract the reduction from the base temperature
• Boiling point = Base temperature - Total reduction
• \(\mathrm{B} = 212 - \frac{\mathrm{x}}{550}\)

Answer: D. \(\mathrm{B} = 212 - \frac{\mathrm{x}}{550}\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret "lowered by" and think temperature increases with altitude instead of decreases.

They reason: "Higher altitude means higher temperature" and create the equation \(\mathrm{B} = 212 + \frac{\mathrm{x}}{550}\). This leads them to select Choice C (\(\mathrm{B} = 212 + \frac{\mathrm{x}}{550}\)).

Second Most Common Error:

Poor TRANSLATE reasoning: Students confuse which number represents the base temperature versus the rate increment.

They mix up \(212°\mathrm{F}\) (the base temperature) and \(550\) feet (the rate increment), thinking \(550°\mathrm{F}\) is the starting temperature. This confusion leads them to select Choice A (\(\mathrm{B} = 550 + \frac{\mathrm{x}}{212}\)) or Choice B (\(\mathrm{B} = 550 - \frac{\mathrm{x}}{212}\)).

The Bottom Line:

This problem tests your ability to translate a real-world rate relationship into mathematical form. The key insight is recognizing that "every 550 feet" creates the fraction \(\frac{\mathrm{x}}{550}\), and "lowered by" means subtraction from the base value of \(212°\mathrm{F}\).