To determine how many machines are needed to stamp 200 envelopes per minute, we need to follow these steps:
1. Determine the rate at which one machine stamps envelopes:
- It's given that one machine can stamp 120 envelopes in 30 minutes.
- First, we find the stamping rate of one machine per minute by dividing the number of envelopes by the time in minutes:
[tex]\[
\frac{120 \, \text{envelopes}}{30 \, \text{minutes}} = 4 \, \text{envelopes per minute}
\][/tex]
2. Determine the number of machines required to meet the target rate:
- We need the machines to stamp 200 envelopes per minute.
- Given each machine stamps 4 envelopes per minute, we can calculate the number of machines required by dividing the target rate by the rate of one machine:
[tex]\[
\frac{200 \, \text{envelopes per minute}}{4 \, \text{envelopes per minute per machine}} = 50 \, \text{machines}
\][/tex]
Therefore, 50 machines, working simultaneously, are required to stamp 200 envelopes per minute. Hence, the correct answer is:
(D) 50 Machines
