3.29 The volume of substance $A$ is half the sum of the volumes of substances $B$ and $C$, and the volume of substance $B$ is $\frac{1}{5}$ of the sum of the volumes of substances $A$ and $C$. Find the ratio of the volume of substance $C$ to the sum of the volumes of substances $A$ and $B$.
3.29 According to the condition, $2 V_{A}=V_{B}+V_{C}$ and $5 V_{B}=V_{A}+V_{C}$. Let $V_{A}=x V_{C}$ and $V_{B}=y V_{C}$. Then we get the system

$\left\{\begin{array}{l}2 x-y=1 \\ -x+5 y=1\end{array}\right.$

from which $x=\frac{2}{3}, y=\frac{1}{3}$. Therefore,

$\frac{V_{C}}{V_{A}+V_{B}}=\frac{1}{x+y}=1$

Answer: 1.