13.169. A crystal, while in the formation stage, uniformly increases its mass. Observing the formation of two crystals, it was noted that the first one over 3 months gave the same mass increase as the second one over 7 months. However, after a year, it turned out that the first crystal increased its initial mass by $4 \%$, and the second - by $5 \%$. Find the ratio of the initial masses of these crystals.
## Solution.

Let the annual increase in mass $x$ be $a$; then the annual increase in mass $y$ is $\frac{3 a}{7}$. We have $a=0.04 x, \frac{3 a}{7}=0.05 y \Rightarrow$ $\Rightarrow \frac{4}{5} \cdot \frac{x}{y}=\frac{7}{3} \Rightarrow x: y=35: 12$.

Answer: $35: 12$.