lets take 1 coin from the 1st set, 2 coins from 2nd set and etc. 10 coins from 10 th set. when we know the total weight, it will be less for 100X than total weight of normal 55 coins. devide the difference on 100 and that is the number of set!

now you can add a step to make it a little easier and just use 9 out of the 10 sets; then follow the same rules, but the total weight you are looking for this time would be 45 instead of 55, which seems a little more practical to me.

If you know the exact weight of the coins why not just put all of the bags on the scale and then take them off one at a time to see which one changes the weight the least