A photocopy machine is initially loaded with 5,000 sheets of paper. The machine starts a large job and copies at a constant rate. After 20 minutes, it has used 30% of the paper. Which of the following equations models the number of sheets of paper, p, remaining in the machine m minutes after the machine started printing?
Correct answer: B. p = 5,000 - 75m
- A. p = 5,000 - 20m
- B. p = 5,000 - 75m
- C. p = 5,000 (0.3)m/20
- D. p = 5,000 (0.7)m/20
Explanation
Choice B is correct because it establishes a linear relationship between the number of sheets remaining and time, based on the constant rate of paper usage calculated from the given data. Initially, there are 5,000 sheets, and 30% of these are used in 20 minutes, equating to 1,500 sheets. Thus, the machine uses 1,500/20 = 75 sheets per minute. The equation p = 5,000 - 75m accurately models the number of sheets remaining after m minutes. Option A incorrectly assumes a usage rate of 20 sheets per minute. Options C and D incorrectly apply an exponential decay model, which is not suitable for this scenario.
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