In the city of Trocalândia, $20 \%$ of the cats think they are dogs and $25 \%$ of the dogs think they are cats. One day, a veterinary psychologist decides to test all the cats and dogs in Trocalândia, finding that $30 \%$ of the total thought they were cats. What proportion of the tested animals were dogs?
Solution

Let $C$ and $G$ be the number of dogs and cats in Trocalandia, respectively. The number of cats that think they are cats is

$$
\frac{80 G}{100}
$$

The number of dogs that think they are cats is

$$
\frac{25 C}{100}
$$

Therefore, the total number of animals that think they are cats is

$$
\frac{80 G+25 C}{100}
$$

According to the veterinary psychologist,

$$
\begin{aligned}
\frac{80 G+25 C}{100}=\frac{30}{100}(G+C) & \Longrightarrow 80 G+25 C=30 G+30 C \\
& \Longrightarrow 80 G-30 G=30 C-25 C \\
& \Longrightarrow 10 G=C
\end{aligned}
$$

Therefore, the proportion of dogs is

$$
\frac{C}{C+G}=\frac{10 G}{10 G+G}=\frac{10}{11}
$$

The final answer is 10/11.