$$3 \frac{6}{7} : \frac{x}{38} = \frac{1}{7}$$
$$\frac{27}{7} : \frac{x}{38} = \frac{1}{7}$$
$$\frac{x}{38} = \frac{27}{7} : \frac{1}{7}$$
$$\frac{x}{38} = \frac{27}{7} \cdot \frac{7}{1}$$
$$\frac{x}{38} = 27$$
$$x = 27 \cdot 38$$
$$x = 1026$$
Ответ: x = 1026.