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## 'Searching for Mean(ing)' printed from http://nrich.maths.org/

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.