Practical problem

[Guest]

Here's my problem;
I have a belt drive grinder that is missing most or all of the pulleys;
The drive motor is 16,000 rpm
The speeds desired are: 42,600, 27,900, 23,400, 12,500, 10,600, 7,000, 5,375, 4,150 and 3,200
The manufacturer lists the following pulleys: .75, 1, 1.2, 2, 3, and 4. I have on the machine pulley #1 which is 0.875 diameter and #3 is 2.233 diameter
The combinations listed on the nameplate are:
driven rpm - drive : driven
42,600 #1.2 #4
27,900 #1 #2
23,400 #2 #3
12,250 #1.2 #1
10,600 #3 #2
7,000 #3 #1.2
5,375 #3 #1
4,150 #3 #.75
3,200 #4 #.75

What is required is the diameters of all of the pulleys given that 16000/(2.233/.875)=6270 instead of 5,375 it's possible that neither #1 and #3 are the correct sizes though #1 is probably correct.
It's been 50+ years since I took my college math so I'm not sure this is even the correct part of the forum to post the question, any help would be appreciated. As well as solving the problem, I'd like to know how it's done.

[laverne3ca]

I posted this problem as a guest, is this the correct place to post this or is there a better branch of mathematics that will be more appropriate? Seems to me that there should be a way to arrive at the solution that's better than trial and error.