Balancing 2

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.

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

so 30 marbles... 42cm +10.5cm = 52.5cm

15 marbles... 52.5 / 2 = 26.25cm

8 marbles ...14cm