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Searching for Mean(ing)

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

Four 3kg weights and one 8kg weight have an average weight of 4kg.
4 3kg qnd 1 8kg weight balancing 5 4kg weights

How many of each weight would you need for the average (mean) of the weights to be 6kg?

If you had other combinations of the 3kg and 8kg weights, what other whole number averages could you make?
What's the smallest?
What's the largest?
Can you make all the whole number values in between?

What if you have a different pair of weights (for example 2kg and 7kg)?
What averages can you now make?

Try other different pairs of weights.

Do you notice anything about your results?
Do they have anything in common?
Can you use what you notice to find, for example, the combination of 17kg and 57kg weights that have an average of 44kg......of 52kg.......of 21kg.....?

Explain an efficient way of doing this.
Can you explain why your method works?
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