Julissa needs at least 100 hours of flight time to get her private pilot certification. If Julissa already has 86...

1. TRANSLATE the problem information

• Given information:
  • Julissa needs at least 100 hours → \(\text{total hours} \geq 100\)
  • She already has 86 hours
  • We need the minimum additional hours → find the smallest value that works

• What this tells us: We're looking for the smallest number to add to 86 to reach at least 100.

2. INFER the mathematical relationship

• Key insight: Total hours = Current hours + Additional hours
• Since total hours must be at least 100: \(\text{Current hours} + \text{Additional hours} \geq 100\)
• Setting up the inequality: \(86 + \mathrm{x} \geq 100\) (where x = additional hours needed)

3. SIMPLIFY by solving the inequality

• Start with: \(86 + \mathrm{x} \geq 100\)
• Subtract 86 from both sides: \(\mathrm{x} \geq 100 - 86\)
• Calculate: \(\mathrm{x} \geq 14\)

Since \(\mathrm{x} \geq 14\), the minimum value for x is exactly 14.

Answer: A. 14

Why Students Usually Falter on This Problem

Most Common Error Path:

Poor TRANSLATE reasoning: Students misunderstand what the question is asking for. They see "86 hours" prominently mentioned and select it as the answer, not recognizing that the question asks for additional hours, not current hours.

This leads them to select Choice C (86).

Second Most Common Error:

Weak INFER skill: Students recognize they need to do something with 100 and 86, but incorrectly think they should add 100 to 86 rather than find the difference. They calculate \(86 + 100 = 186\), thinking this represents some kind of total requirement.

This may lead them to select Choice D (186).

The Bottom Line:

This problem tests whether students can distinguish between "current amount," "total needed," and "additional amount needed." The key challenge is carefully reading what the question asks for and setting up the correct mathematical relationship.