## Task 5 - 250835

The following problem is from Leo Nikolayevich Tolstoy (1828 - 1910), a prominent Russian writer:

Reapers are to mow two meadows. In the morning, all of them started mowing the larger meadow. However, from noon of that day, they divided the work differently: half of the reapers continued mowing the first meadow, which they finished by evening. The other reapers moved to mow the second meadow, whose area was equal to half of the first, and worked until evening. Now, a remainder was left on the second meadow, which one reaper alone would need an entire day to complete.

How many reapers were at work on the first day?

Note: It is assumed that each reaper mows the same area in the morning as in the afternoon, and that the work performance of all reapers is the same.
If on the first day $x$ mowers were at work, then:

The mowing of the second meadow is half the daily performance of $\frac{x}{2}$ mowers, increased by the daily performance of one mower. The mowing of the first meadow is twice this performance; it is thus the daily performance of $\frac{x}{2}$ mowers, increased by the daily performance of two mowers.

On the other hand, the mowing of the first meadow was half the daily performance of $x$ mowers, increased by half the daily performance of $\frac{x}{2}$ mowers.

$$
\frac{x}{2}+2=\frac{1}{2} \cdot x+\frac{1}{2} \cdot \frac{x}{2} \quad \Rightarrow \quad x=8
$$

Therefore, eight mowers were at work on the first day.