1. A person, every day, first spent 100 denars, and then earned $\frac{1}{3}$ of the remaining. After three days, he found that the initial amount of money had doubled.

How much money did the person have at the beginning?
Solution. Let the person initially have $x$ denars. At the end of the first day, he had

$$
x-100+\frac{x-100}{3}=\frac{4}{3}(x-100) \text { denars. }
$$

At the end of the second day, he had $\frac{4}{3}\left(\frac{4}{3}(x-100)-100\right)$ denars. At the end of the third day, he had $\frac{4}{3}\left(\frac{4}{3}\left(\frac{4}{3}(x-100)-100\right)-100\right)$ denars. According to this:

$$
\frac{4}{3}\left(\frac{4}{3}\left(\frac{4}{3}(x-100)-100\right)-100\right)=2 x
$$

The solution to this equation is $x=1480$ denars.