Balancing 1

Stage: 3 Challenge Level: Challenge Level:1

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!).


Published January 2006.