4B. In the goldsmith's workshop, a mixture of $5 \mathrm{~kg}$ needs to be made in which the ratio of the quantities of gold and silver is 22:41. In stock, there are two mixtures. In one, the quantities of gold and silver are in the ratio $4: 5$, and in the second $2: 5$. How much should be taken from each mixture to obtain the desired mixture?
Solution. In the new mixture of $5 \mathrm{~kg}$, there needs to be $5 \cdot \frac{22}{63} \mathrm{~kg}$ of gold. Let's take $x$ $\mathrm{kg}$ from the first and $y \mathrm{~kg}$ from the second mixture.

The amount of gold that needs to be obtained in this way is $x \cdot \frac{4}{9} + y \cdot \frac{2}{7}$. According to the conditions of the problem, we get the system

$$
\left\{\begin{array}{l}
x \cdot \frac{4}{9} + y \cdot \frac{2}{7} = 5 \cdot \frac{22}{63} \\
x + y = 5
\end{array}\right.
$$

whose solution is $x=2$ and $y=3$.

Therefore, we need to take $2 \mathrm{~kg}$ from the first and $3 \mathrm{~kg}$ from the second mixture.