13.090. A piece of alloy of copper with tin has a total mass of 12 kg, containing $45 \%$ copper. How much pure tin should be added to this piece of alloy so that the resulting new alloy contains $40 \%$ copper?
## Solution.

Initially, the alloy contained $12 \cdot 0.45=5.4$ kg of copper. After adding tin, these 5.4 kg of copper make up $40 \%$. Therefore, the total mass of the alloy is $\frac{5.4}{0.4}=13.5$ kg. Thus, $13.5-12=1.5$ kg of tin needs to be added.

Answer: 1.5 kg.