Problem 3. Jana asked Philip how much the fish his father caught weighed. Philip replied: The head together with the tail weighs $3 \mathrm{~kg}$, the head together with the body weighs $7 \mathrm{~kg}$, and the body together with the tail weighs $8 \mathrm{~kg}$. How much does the fish weigh?
Solution. First method. If we add the given weights, then in the sum, the weights of the head, tail, and body will each be counted twice. According to this, the weight of the fish is half of the calculated sum.

According to this, if $x$ is the weight of the fish, then $x=18: 2=9 \text{ kg}$.

Second method. Let $G$ be the weight of the head, $O$ be the weight of the tail, and $T$ be the weight of the body. From the conditions of the problem, we have:

$$
G+O=3, \quad G+T=7, \quad T+O=8
$$

If we add the left and right sides, we get:

$$
\begin{aligned}
& G+O+G+T+T+O=18 \\
& 2 G+2 O+2 T=18 \\
& 2(G+O+T)=18
\end{aligned}
$$

From this, $G+O+T=9$, so the fish weighs $9 \text{ kg}$.