If in the city there were 3000 more residents; then, each resident would have paid 10 forints less in tribute to the enemy; if, however, there were 1000 fewer residents; then each would have paid 10 forints more. - How many residents were there, how much did one pay, and how much did the entire city pay?
Let $x$ be the number of residents and the tax per resident $y$ forints. According to the problem,

$$
(x+3000)(y-10)=x y
$$

and

$$
(x-1000)(y+10)=x y
$$

Rearranging:

$$
\begin{aligned}
& 10 x-3000 y=-30000 \\
& 10 x-1000 y=10000
\end{aligned}
$$

Subtracting (1') from (2')

$$
\begin{aligned}
2000 y & =40000 \\
y & =20 \\
10 x & =10000+20000=30000 \\
x & =3000
\end{aligned}
$$

Thus,

The city had 3000 residents, each resident paid 20 forints in tax, and the entire city paid 60000 forints.

Barabás Ildikó (Nyíregyháza, Zrínyi Ilona g. II. o. t.)