Among well-performing workers, a certain amount was divided equally as a reward: If there were 5 fewer workers to be rewarded, then each worker would receive exactly as much more as they would receive less if the number of workers to be rewarded were increased by 7. How many workers received the reward?
Consider the amount to be distributed as a unit, and let the number of workers be $x$. The amount per worker in the three cases is thus $\frac{1}{x}, \frac{1}{x-5}, \frac{1}{x+7}$. According to the problem,

$$
\frac{1}{x-5}-\frac{1}{x}=\frac{1}{x}-\frac{1}{x+7}
$$

Bringing both sides to a common denominator,

$$
\frac{x-(x-5)}{x(x-5)}=\frac{(x+7)-x}{x(x+7)}
$$

Multiplying both sides by $x$ ($x \neq 0$),

$$
\frac{5}{x-5}=\frac{7}{x+7}
$$

from which

$$
x=35 \text {. }
$$

Kálmán Edit (Kiskunhalas, Sziládi Áron g. II. o. t.)