how do i solve this problem step for step to find the equation?
Suppose you manage a juice factory. One of your machines fills 850 bottles
per minute. Each day it takes 30 min to get the machine started after an hour for maintenance.
It appears that there may be some information missing from problem description. Let's assume that the question is asking us for how many bottles of juice are produced after a certain number of minutes. In this case, we know that the factory produces 850 bottles per minutes. So, we can let m = minutes and we know that the production will be 850m.
Therefore, we start the equation by saying that once the machines are up and running, the number of bottles of juice = the number of minutes in production times 850
b = 850m
However, we will probably measure minutes from when we start the production run. Therefore, we will not get 850 bottles per minute for all of the minutes because there are some things that we have to do on a one-time basis per production run. It takes 30 minutes to get the machine started and 60 minutes for maintenance. So, we have to subtract 850(90) from our production numbers because we are baisically out-of-commission during the first 90 minutes.
Our final equation would be:
b = 850m - 76,500
Said in English, "The number of bottles of juice produced after m minutes would be 850 per minute minus 76,500 that were not produced during the first 90 minutes of pre-production setup."