4) A bucket full of sand weighs a total of $9 \mathrm{~kg}$, when half full of sand it weighs $5 \mathrm{~kg}$. How much does the empty bucket weigh?

$\begin{array}{llll}\text { (A) } 0.5 \mathrm{~kg} & \text { (B) } 1 \mathrm{~kg} & \text { (C) } 2 \mathrm{~kg} & \text { (D) } 2.5 \mathrm{~kg}\end{array}$

(E) the weight of the bucket cannot be determined.
4) The answer is $\mathbf{( B )}$.

Let $x$ be the weight of the empty bucket and $y$ be the weight of the sand. We have

$\left\{\begin{array}{l}x+y=9 \\ x+\frac{y}{2}=5\end{array} \quad\right.$ from which $\quad x=1 \mathrm{~kg}$ and $y=8 \mathrm{~kg}$.