Explanation of "Loan Repayment" Solution

Problems and Contests
#1

One of the harder problems, according to USACO.guide, is Loan Repayment. I have looked over the official editorial and don’t fully understand what the solution encompasses. I would be grateful for any help or further explanation as to what to do and why it works. Thanks so much!

Here is the link to the problem: Loan Repayment Problem

Here is the link to the official solution: Loan Repayment Solution

#2

Use some math to compute the max number of days numdays such that FJ gives Bessie the same amount of milk on each of those days.

#5

Not sure what you mean. In the solution, you can see that FJ gives Bessie y gallons of milk for numdays.