A copy machine, working at a constant rate, makes 35 copies per minute. A second copy machine, working at a constant rate, makes 55 copies per minute. Working together at their respective rates, how many copies do the two machines make in half an hour?
90
2,700
4,500
5,400
324,000
The answer choices are quite far apart in this problem, indicating that you can probably estimate.
The question asks how many copies the two machines can make together in half an hour. The second machine produces more copies per minute, so start there. In 30 minutes, the second machine alone would produce (55)(30) copies. Call it (60)(30) to make the math easier. So the second machine will produce about 1,800 copies in 30 minutes.
The first copy machine will produce fewer copies than the second. The two working together must produce more than 1,800 copies, but fewer than twice as many, or 3,600. Eliminate answer (A) for being too low and answers (C), (D), and (E) for being too high.
Alternatively, when two machines are working together to fulfill a job, add their individual rates to find their combined rate. The first makes 35 copies per minute and the second makes 55 copies per minute:
35 + 55 = 90 copies per minute combined
The question asks how many copies the machines make in half an hour, which is equivalent to 30 minutes. If the machines can make 90 copies in 1 minute, then they can make (90)(30) copies in 30 minutes.
When multiplying values with zeros at the end, first ignore the zeros and just multiply the actual values:
90 × 30:
9 × 3 = 27
Then add back in the missing zeros. In this case, there are two zeros, so 27 becomes 2,700.
The correct answer is (B). Answer (D) is a great trap answer for those who solve via a more textbook approach—it reflects how many copies the two machines would make in a full hour rather than half an hour.