Balancing 2

Meg and Mo have been distracted from their game of Marbles by the balance on which they hang their pouches of marbles between games.

They discover that they can make their pouches balance with Meg's pouch $60$cm from the centre, and with $10$ marbles in Mo's pouch.

Use the interactivity to explore this further.

Full Screen Version

Fill in the table below showing how many marbles Mo needs in her pouch to balance Meg's pouch when it is in various different places away from the centre.

Without using the interactivitiy, can you now work out how many marbles Mo would need in her pouch to balance with Meg's?

Try to explain how you worked it out.

They take a break from playing with the balance to play another quick game of Marbles, after which they both have different numbers of marbles and someone has sneakily altered the balance.

They find that when they hang their pouches on the new balance, the two pouches balance when Meg has $12$ marbles, and Mo has her pouch $21$cm from the centre.

Use the interactivity to explore this further.

This time, Mo is going to move her pouch as Meg adds and removes marbles from her own pouch. Fill in the table below to show where Mo needs to move her pouch.

Without using the interactivitiy, can you now work out where Mo would need to place her pouch to balance with Meg's?

Try to explain how you worked it out.