The particular problem with this puzzle is that the bag can be any weight and any distance from the centre, making two factors to consider. However, after experimenting with the scales, I found there was a relation between the weight and distance of one bag and that of the other bag when the scales balanced. I started to work with the numbers in my head, and I found that the relation was between the products of the two pairs of numbers. In other words: weight of Meg's bag x distance from centre of Meg's bag = weight of Mo's bag x distance from centre of Mo's bag. Looking at a first class lever (e.g. a see-saw), you can see that the further away the effort (Meg's bag in this case) is from the fulcrum (i.e. middle of the scales), the less force (weight in this case) is needed to lift the load (Mo's bag in this case). This means the bigger the distance and the heavier the bag, the more weight can be lifted, which helps to create a unit of measure that we can compare instead of two separate units. Because both units have to be bigger to lift more weight, we have to multiply them together to get our new unit. We can call this unit, 'effective weight', because it is the weight of the bag that it would balance with if the bag could be any distance away from the middle of the scales without its own effective weight changing. In other words, if two bags have the same effective weight, they will balance. To make it clear what the effective weight of a bag is, this is the formula: effective weight = weight x distance from centre. Going back to the problem, the unit of effective weight is marbles (weight) x cm (distance from middle of scales), and this arms us with a solution to the problem. A quick glance at Mo's bag tells us that the effective weight is 800 (marbles x cm)*, meaning that any bag with an effective weight of 800 (marbles x cm)* will balance with it. Once you know this, all you need is one of the measurements and filling in the tables is a doddle. To show you, the filled in tables are as follows (answers in red):

Distance
from the		Number
centre			of marbles
100 cm		8
50 cm			16
25 cm			32
40 cm			20

200 cm		4
20 cm			40
32 cm			25
x cm			800 ÷ x
(800 ÷ x) cm		x

I suspect the last two, those involving 'x', were probably put in to see if you understood the general rule, and could therefore solve any problem of this type. Incidentally, the highest number of marbles possible on the interactivity is 32, meaning the nearest possible distance to the centre whilst keeping the bags balanced is 25 cm (see chart, above).

P.S. If 'effective' isn't a word, sorry!

*Note: The units are kept in brackets so you do not confuse them with the surrounding text.