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?

Options

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)`

Answer

B

Explanation

Since the machine copies at a constant rate, the relationship between p, the number of sheets of paper remaining, and m, the time in minutes since the machine started printing, is modeled by a linear equation. The initial number of sheets of paper is given as 5,000. It is also given that the machine used 30% of those 5,000 sheets in 20 minutes, so it used 0.30 × 5,000 = 1,500 sheets in 20 minutes. Therefore, the number of sheets used per minute is `(1,500)/20=75`. To determine the number of sheets of paper used m minutes after the machine started printing, multiply 75 by m, which gives 75m. Therefore, a linear equation modeling this relationship is the number of sheets remaining equals the initial number of sheets of paper minus the number of sheets of paper used m minutes after the machine started printing, which is p = 5,000 − 75m. Choice A is incorrect and may be the result of using the given number of minutes, 20, as the rate at which the copy machine uses paper. However, the rate is 75, not 20, sheets per minute. Choices C and D are incorrect because they aren’t linear equations, they assume that the copy machine prints at a nonconstant rate.