Weight of a bucket when filled fully with water is 17 kg. If the weight of the bucket when half filled with water is 13.5 kg, what is the weight of empty bucket?

$$\eqalign{ & {\text{Bucket}} + {\text{full water}} = {\text{17 kg}} \cr & \underline {{\text{Bucket}} + \frac{1}{2}{\text{water}} = 13.5{\text{ kg}}} \to \left( {{\text{Subtract}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{1}{2}{\text{water}} = 3.5\,{\text{kg}} \cr & \therefore {\text{Water}} = 2 \times 3.5 = 7\,{\text{kg}} \cr & \therefore {\text{Weight of empty bucket}} \cr & = 17 - 7 = 10{\text{ kg}} \cr} $$