Maria's course grade is calculated using weighted averages where the weights sum to 100%: homework counts for 40%, quizzes count...

1. TRANSLATE the problem information

• Given information:
  • Homework weight: \(40\% = 0.40\)
  • Quiz weight: \(30\% = 0.30\)
  • Final exam weight: \(30\% = 0.30\)
  • Homework score: 85 points
  • Quiz score: 80 points
  • Final exam score: F (unknown)
  • Need: Course grade \(\geq 85\)

2. INFER the mathematical approach

• This is a weighted average problem, not a simple average
• Course grade = sum of (weight × score) for each component
• "At least 85" means we need \(\geq 85\), creating an inequality

3. TRANSLATE into mathematical notation

• Course Grade = \(0.40(85) + 0.30(80) + 0.30(F)\)
• For at least 85: \(0.40(85) + 0.30(80) + 0.30(F) \geq 85\)

Answer: A

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skills: Students confuse weighted averages with simple averages, thinking all scores should be added equally.

They might set up: \(\frac{F + 85 + 80}{3} \geq 85\), forgetting that different categories have different importance (weights). This leads them to select Choice C.

Second Most Common Error:

Poor TRANSLATE execution: Students forget to convert percentages to decimals, keeping them as whole numbers.

They might write: \(40F + 30(85) + 30(80) \geq 85\), which incorrectly treats 40% as 40 instead of 0.40. This leads them to select Choice D.

The Bottom Line:

This problem tests whether students understand that "counts for 40%" means multiply by 0.40, not 40, and that weighted averages give different importance to different components rather than treating all scores equally.