13.045. A piece of copper and zinc alloy weighing 36 kg contains $45 \%$ copper. What mass of copper needs to be added to this piece so that the resulting new alloy contains $60 \%$ copper?
Solution.

Initially, the alloy contains $36 \cdot 0.45 = 16.2$ kg of copper. Let $x$ kg of copper be added. Then the mass of the new alloy is $36 + x$ kg, and the mass of copper in it is $16.2 + x$ kg. According to the condition, $16.2 + x = (36 + x) \cdot 0.6$, from which $x = 13.5$ kg.

Answer: 13.5 kg.