Determinants & Inverses · Medium problem

Three alloys are combined in amounts $x,y,z$ (kg) to make $100$ kg of a new blend. Alloy $x$ is $60\%$ copper, $y$ is $30\%$ copper, and $z$ is $10\%$ copper; the blend must contain $41$ kg of copper. Also, $20$ kg more of alloy $x$ is used than alloy $y$. Find $z$.