The ratio method and the algebraic method are techniques that need to be developed to be able to complete the question provided by mh1 and for more complex questions.
Practical demonstrations are good for explaining the concepts behind the question, but a ten year old should have advanced from counting and dividing money into appropriate proportions to learning a mathematical approach.
The original starting amounts were,
It would be necessary to ensure that the range of coins that produces the above values could be re-arranged to provide the new values of,
Using 168 1p pieces would be impractical to demonstrate the exercise to the student.
So, what would be the minimum number of coins required to demonstrate the question? and what would be the minimum range of coins required?
A= 50p, 20p, 20p, 5p, 2p, 1p, 1p
B= 20p, 20p
C= 20p, 5p, 2p, 2p
With the exchanges complete,
A= 50p, 20p, 20p, 5p, 1p
B= 20p, 20p, 5p, 2p, 1p
C= 20p, 2p, 2p
I would prefer to use more simple ratio or algebra based questions to demonstrate how to work out the question. Starting by using two values rather than three.
Explanation, Example, Exercise, Evaluation, Extension