A proportionality puzzle: If half of $5$ is $3$, then what's one-third of $10$? My professor gave us this problem.

In a foreign country, half of 5 is 3. Based on that same proportion, what's one-third of 10?

I removed my try because it's wrong.

Given that
$$
\begin{equation}
\tag{1}
\text{half of }5 = 3
\end{equation}
$$
this implies that 
$$
\begin{equation}
\tag{2}
\text{half of }10 = 6
\end{equation}
$$
$(2)$ then says that half of $1 = 0.6$ and therefore 
$$
\begin{equation}
\tag{3}
\frac{1}{3}\text{ of }1 = \frac{0.33 \times 0.6}{0.5} = 0.396
\end{equation}
$$
There for since $\frac{1}{3}$ of $1$ corresponds to $.396$ thus $\frac{1}{3}$ of $10 = 3.96$
Answer: $3.96$
