### Balancing 1

Meg and Mo need to hang their marbles so that they balance. 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 2

##### Stage: 3 Challenge Level:

Congratulations to Kyla and Ashley from the North London Collegiate School for Girls who explained how to work out the answers:

For every 60cm that Meg's bag is moved away from the middle, Mo's bag has to have 10 marbles. So if you put Meg's bag 30cm away from the middle the answer for Mo's bag has to be half the amount of marbles that she had to start with, because 30cm is half of 60cm (the distance you had to start with).
You do the same thing if you are multiplying. It is all to do with ratio.

Alice and Alex from The Mount School in York sent in a really lovely solution to the question, in which they explain their calculations.

 Meg Mo 60cm 10 marbles 30cm 5 marbles 90cm 15 marbles

 Meg Mo 120cm 20 marbles 12cm 2 marbles 48cm 8 marbles 24cm 4 marbles 75cm 12.5 marbles

For every 30cm there are 5 marbles.

30cm * 4 = 120cm
5 marbles * 4 = 20 marbles

120cm / 10 = 12cm
20 marbles / 10 = 2 marbles

12cm * 4 = 48cm
2 marbles * 4 = 8 marbles

12cm * 2 = 24cm
2 marbles * 2 = 4 marbles

60cm...10 marbles; 15cm ...2.5 marbles
75cm...10 + 2.5 = 12.5 marbles

 Meg Mo 12 marbles 21cm 24 marbles 42cm 16 marbles 28cm 8 marbles 14cm

 Meg Mo 30 marbles 52.5cm 15 marbles 26.25cm 2 marbles 3.5cm x marbles 1.75 x cm

24 marbles... 42cm

6 marbles... 42/4 = 10.5cm
so 30 marbles... 42cm +10.5cm = 52.5cm

15 marbles... 52.5 / 2 = 26.25cm

8 marbles ...14cm
so 2 marbles... 14 / 4 = 3.5cm