Imagine you have a large supply of 3kg and 8kg weights.

Can you see how the picture below can be used to explain why two 3kg weights and three 8kg weights have a mean weight of 6kg?

What's the smallest possible mean?

What's the largest?

Now explore some different pairs of weights (for example 2kg and 7kg).

What do you notice about your results?

Can you use what you notice to find the combination of 17kg and 57kg weights that have a mean weight of 44kg......of 52kg.......of 21kg.....?

Explain an efficient way of doing this.

Can you explain why your method works?

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