## Task 3 - 100823

For a piece of copper-zinc alloy weighing $216 \mathrm{kp}$, a buoyancy (weight loss) of $26 \mathrm{kp}$ was measured in water.

It is known that copper loses $\frac{1}{9}$ of its original weight when immersed in (distilled) water, and zinc loses $\frac{1}{7}$ of its original weight.

Determine the percentage weight proportion of copper and zinc in the given alloy! (The quantities to be determined should be rounded to the nearest whole percent).
Let the weight of the copper part in the alloy be $x$ kp. Then the weight of the zinc part is $(216-x) \mathrm{kp}$.

When immersed in water, the weight loss of the copper part is $\frac{1}{9} x \mathrm{kp}$ and that of the zinc part is $\frac{1}{7}(216-x) \mathrm{kp}$. Therefore, we have:

$$
\frac{1}{9} x+\frac{1}{7}(216-x)=26
$$

from which we get $7 x+9 \cdot(216-x)=63 \cdot 26$, thus $x=153$.

Therefore, the weight of the copper part can only be $153 \mathrm{kp}$, and the weight of the zinc part can only be $216 \mathrm{kp}-153 \mathrm{kp}=63 \mathrm{kp}$.

Since $153: 216 \approx 0.708$, the percentage of copper is approximately $71\%$, and that of zinc is approximately $29\%$.