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ACT (Enhanced)MathematicsMedium

A quality control manager is inspecting a batch of 500 items. The number of defective items (d) found is modeled by the linear equation d = 0.08n + 5, where n is the number of items inspected. What percentage of the first 100 items inspected are expected to be defective?

  1. A5%
  2. B13%
  3. C8%
  4. D10%
Show answer & explanation

Correct answer: B. 13%

First, calculate the expected number of defective items when n=100 using the given linear model. Then, divide this number by the total items inspected (100) and multiply by 100 to get the percentage.

Why the other options are wrong

  • A. Incorrect. This is the constant term, representing initial defects or a baseline.
  • C. Incorrect. This only accounts for the slope (0.08), ignoring the constant term (+5).
  • D. Incorrect. This would be 10 defective items, possibly by miscalculation or misinterpreting the slope.

Percentage from Linear Model

To find the percentage of a quantity from a linear model, first calculate the quantity using the model, then divide by the total and multiply by 100%.

  • Evaluate the linear model for the given input.
  • Divide the output by the total number of items.
  • Multiply the result by 100 to express as a percentage.

Memory trick: Follow the 'Linear Path' to 'Calculate' and then 'Percent-age'.

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