ACT (Enhanced)MathematicsHard
A quality control manager is inspecting a batch of 500 items. The number of defective items (d) found in the batch is modeled by the equation d = 0.02n + 5, where n is the number of items inspected. If the manager inspects all 500 items, what percentage of the inspected items are defective?
- A3%
- B3.5%
- C4%
- D5%
Show answer & explanationAnswer & explanation
Correct answer: C. 4%
First, calculate the number of defective items by substituting n=500 into the equation. Then, calculate the percentage of defective items by dividing the number of defective items by the total number of items inspected and multiplying by 100.
Why the other options are wrong
- A. This results from a miscalculation of the number of defective items or percentage.
- B. This is a plausible distractor based on a slight miscalculation.
- D. This is the constant term in the equation, not the percentage of defective items.
Percentage Calculation from Linear Model
Calculating a percentage based on a value derived from a linear equation relative to a total quantity.
- Evaluate the linear function to find the count of interest.
- Percentage = (Part / Whole) * 100%.
- Ensure units are consistent before calculating percentage.
Memory trick: Linear output first, then divide by whole, for a percentage burst!