2. Last year, 9900 umbrellas were reported to the lost and found department. Some people lost exactly one umbrella, but there were also those who lost more than one umbrella. Specifically, $4 \%$ of them lost exactly two umbrellas, $2.5 \%$ lost three umbrellas, $0.5 \%$ lost eight umbrellas, and the rest lost one umbrella. How many people lost at least one umbrella?
Solution. If we denote the number of people who lost umbrellas by $x$, then from the condition of the problem we have that $0.04 x$ lost two umbrellas each, $0.025 x$ lost three umbrellas each, $0.005 x$ lost eight umbrellas each, and

$$
(1-(0.04+0.025+0.005) x=0.93 x
$$

lost one umbrella each. Therefore, the number of lost umbrellas is

$$
2 \cdot 0.04 x+3 \cdot 0.025 x+8 \cdot 0.005 x+1 \cdot 0.93 x=1.125 x
$$

so $1.125 x=9900$, or $x=\frac{9900}{1.125}=8800$. Thus, last year 8800 people lost at least one umbrella.