The atmospheric pressure at sea level is 14.7 pounds per square inch (psi). For each 100 feet of altitude gained...

1. TRANSLATE the problem information

• Given information:
  • Sea level pressure: 14.7 psi
  • Pressure decrease: 0.05 psi for every 100 feet of altitude
  • Target altitude: 7,800 feet above sea level
• Need to find: Atmospheric pressure at 7,800 feet

2. INFER the solution strategy

• Since pressure decreases by 0.05 psi for each 100-foot interval, I need to:
  • First find how many 100-foot units are in 7,800 feet
  • Then calculate the total pressure decrease
  • Finally subtract this from the starting pressure

3. Calculate the number of 100-foot units

• Divide the total altitude by the unit interval:
  \(7,800 \div 100 = 78\) units

4. SIMPLIFY to find total pressure decrease

• Multiply the number of units by the pressure decrease per unit:
  \(0.05 \times 78 = 3.9\) psi

5. SIMPLIFY to find final pressure

• Subtract the total decrease from sea level pressure:
  \(14.7 - 3.9 = 10.8\) psi

Answer: B. 10.8

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students may skip the unit conversion step and multiply 7,800 × 0.05 directly, treating the rate as "0.05 psi per foot" instead of "0.05 psi per 100 feet."

This gives them:
\(14.7 - (7,800 \times 0.05)\)
\(= 14.7 - 390\)
\(= -375.3\) psi
which is clearly impossible. This leads to confusion and guessing among the answer choices.

Second Most Common Error:

Poor TRANSLATE reasoning: Students may misunderstand the direction of pressure change and add the pressure decrease instead of subtracting it.

Following correct calculations but adding:
\(14.7 + 3.9 = 18.6\) psi
Since this value doesn't match any answer choice, this leads to confusion and random selection.

The Bottom Line:

This problem tests students' ability to work with unit rates and proportional reasoning. The key insight is recognizing that the rate applies to 100-foot intervals, not individual feet, making the initial division step crucial for success.