Balancing 1

Meg and Mo are playing Marbles together. After each game, they each put their marbles in a pouch and hang the pouches on a balance while they go off for a snack.

After their first game, they each have the same number of marbles. Meg puts hers in the pouch 50cm to the left of the centre, and Mo puts hers 50cm to the right of the centre. Does this balance?

Suppose that when they come back, Meg moves her pouch to be 80cm away. Find where Mo must put her pouch so that it still balances. 

If Meg moves her pouch to be 25cm from the pivot, find where Mo must put her pouch.

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Meg wins the next game, and since she and Mo are playing for keeps, she now has more marbles than her friend. 

They discover (by experimenting) that if Meg puts her pouch 30cm from the centre and Mo puts hers 50cm from the centre then the pouches balance. 

Fill in the table below so that when the pouches are at the distances shown, they balance.

 

Can you work out the distances from the centre in the table below that Meg and Mo must put their pouches so that they balance?
 

Try to explain how you worked it out.