### Balancing 2

Meg and Mo still need to hang their marbles so that they balance, but this time the constraints are different. Use the interactivity to experiment and find out what they need to do.

### Balancing 3

Mo has left, but Meg is still experimenting. Use the interactivity to help you find out how she can alter her pouch of marbles and still keep the two pouches balanced.

# Balancing 1

##### Stage: 3 Challenge Level:

Congratulations to Debbie and Fiona, Catriona and Ellie from The Mount School in York who completed full solutions to this problem:

 Meg Mo 30cm 50cm 60cm 100cm 45cm 75cm 15cm 25cm

 Meg Mo 90cm 150cm 24cm 40cm 36cm 60cm 20cm 100/3 cm 72/5 cm 24cm

 Meg Mo 10 marbles 6 marbles 20 marbles 12 marbles 5 marbles 3marbles 15marbles 9 marbles

 Meg Mo 30marbles 18 marbles 12 marbles 36/5 marbles 35/3 marbles 7 marbles

Emma, also from The Mount School, offered the following explanation of how to work on these problems:

You start by finding out how to even the balances out. This is how:

It tells you that Meg has 10 marbles and Mo has 6. Then it tells you to put Meg's bag at 30cm and Mo's bag at 50cm. Then you work it out by doing this:

 Meg Mo 10 marbles 6 marbles 30cm 50cm

Meg: 10 x 30 = 300

Mo: 6 x 50 = 300

When you multiply the number of marbles in the bag by the distance from the pivot point you get the same answer on both sides.

Catriona and Ellie showed how they used this insight to complete the second table (when Meg had 10 marbles and Mo had 6 marbles):
We worked this out by doing:

10 * 90cm = 900
6 * 150cm = 900

10 * 24cm = 240
6 * 40cm = 240

We tried this method with all the other numbers.

This means that if we know one of the numbers we can work out the other.
e.g. 10 *___ = 6 *24 = 144
If we do 144/10 = 14.4 we have found the missing number (14.4!).