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Searching for Mean(ing)

Age 11 to 14 Challenge Level:

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

Two 3kg weights and three 8kg weights have a mean weight of 6kg.

Can you find other combinations of 3kg and 8kg weights whose mean weight is a whole number of kg?

What's the smallest?
What's the largest?

Can you make all the whole numbers in between?

What if you have a different pair of weights (for example 2kg and 7kg)?
Which whole numbers is it possible to have as the mean weight now?

Try other different pairs of weights.

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?
Click here for a poster of this problem.