In a company, a certain amount of money, rounded to the nearest hundred, is to be distributed among four employees as a bonus. They are informed that they can choose between two principles of distribution. According to the first principle, the amount is divided in proportion to their monthly salaries, and according to the second principle, it is divided in proportion to the years they have worked. - Each employee voted for the principle that was more favorable to them, so the vote did not result in a decision. Finally, they agreed that each employee would receive the average of the bonus according to the two principles, rounded to the nearest $10 \mathrm{Ft}$. This way, the youngest received $980 \mathrm{Ft}$. How much did the others receive, if they have been working for 14, 17, 21, and 31 years, respectively, and their current salaries are $1500 \mathrm{Ft}, 1600 \mathrm{Ft}, 1800 \mathrm{Ft}$, and $2300 \mathrm{Ft}$, respectively?
If the reward amount were to be divided in proportion to the payments, then the individual workers would receive 15/72, 16/72, 18/72, and 23/72 of the total amount, respectively. In the case of distribution in proportion to the number of years worked, they would receive 14/83, 17/83, 21/83, and 31/83 of the total amount, respectively. The average of these two fractional parts is

$$
\frac{1}{2}\left(\frac{15}{72}+\frac{14}{83}\right)=\frac{2253}{11952}, \quad \frac{2552}{11952}, \quad \frac{3006}{11952}, \quad \frac{4141}{11952}
$$

The rewards paid to the workers according to the agreement are obtained by multiplying these averages by the total amount $x$ to be distributed, and rounding the products to the nearest 10 Ft.

The reward for the youngest worker, calculated by the said multiplication, had to fall between 975 and 985 Ft, because according to the announced rounding rule, 980 Ft results from these values. Therefore,

$$
975 \leq \frac{2253}{11952} x \leq 985
$$

(Multiplying by the reciprocal of the coefficient of $x$ on both sides, we get)

$$
5172 \frac{684}{2253} \leq x \leq 5225 \frac{795}{2253}
$$

(Since the multiplier used is positive).

Among the limits obtained for $x$, there is only one round hundred, so $x=5200 \mathrm{Ft}$.

Using this value of $x$, the rewards for the other three workers, according to the above calculation principle, are 1110 Ft, 1310 Ft, and 1800 Ft, respectively. The adjustments made during rounding, both up and down, balance each other out, and the total amount of the rewards paid is 5200 Ft.