Problem 3. A native from the Tanga-Tanga tribe could, in natural exchange, receive 2 drums, 3 wives, and one leopard skin for 111 arrows. Two leopard skins were valued 8 arrows less than 3 drums and 4 wives. How many arrows did a drum, a wife, and a leopard skin cost separately, if a leopard skin required an even number of arrows? (Each of these items costs a whole number of arrows.) Answer: 20, 9, 44.
Solution. Let the required costs be $-x, y$ and $z$. The condition gives the system

$$
\left\{\begin{aligned}
2 x+3 y+z & =111 \\
3 x+4 y-2 z & =8
\end{aligned}\right.
$$

By adding twice the first equation to the second, we get that $7 x+10 y=230$. It is clear that $x$ must be divisible by 10. Therefore, $x$ can be 30, 20, or 10.

However, from the second equation of the system, it is clear that for $z$ to be even, $x$ must be divisible by 4. Thus, $x=20, y=9, z=44$.