13.309. There are two gold and silver alloys. In one alloy, the quantities of these metals are in the ratio $1: 2$, in the other - $2: 3$.

How many grams should be taken from each alloy to obtain 19 g of an alloy in which gold and silver are in the ratio 7:12?
Solution.

Let $x$ (g) be the amount of the first alloy taken, which contains $\frac{1}{3} x$ gold and $\frac{2}{3} x$ silver. According to the problem, we have the system

$$
\left\{\begin{array}{l}
x+y=19 \\
\frac{1}{3} x+\frac{2}{5} y=\frac{7}{12}\left(\frac{2}{3} x+\frac{3}{5} y\right), \text{ from which } x=9(\mathrm{g}), y=10(\mathrm{g})
\end{array}\right.
$$

Answer: 9 and 10 g.