## Task B-1.3.

Marko spent 100 euros after receiving his salary. Five days later, he won $\frac{1}{4}$ of the remaining amount from his salary in a lottery and spent another 100 euros. After fifteen days, he received $\frac{1}{4}$ of the amount he had at that time and spent another 100 euros. In the end, he had 800 euros more than he had at the moment he received his salary. What was Marko's salary?
## Solution.

Let $x$ be the amount of Marko's salary. After spending 100 euros, Marko has an amount of $x-100$ euros.

After five days, he received a quarter of the remaining amount, which is $\frac{1}{4} \cdot (x-100)$ euros. After spending another 100 euros, he then has

$(x-100) + \frac{1}{4} \cdot (x-100) - 100 = \frac{5}{4} x - 225$ euros.

After fifteen days, he received $\frac{1}{4} \cdot \left(\frac{5}{4} x - 225\right)$ euros, so he then has a total of $\frac{5}{4} x - 225 + \frac{1}{4} \left(\frac{5}{4} x - 225\right) = \frac{5}{4} \left(\frac{5}{4} x - 225\right)$ euros.

Then he spends another 100 euros and ends up with 800 euros more than he started with, which we write as $\frac{5}{4} \left(\frac{5}{4} x - 225\right) - 100 = 800 + x$.

Then we have:

$$
\begin{aligned}
\frac{25}{16} x - x & = 800 + 100 + \frac{1125}{4} \\
\frac{9}{16} x & = 900 + \frac{1125}{4} \\
9 x & = 18900 \\
x & = 2100
\end{aligned}
$$

Therefore, the amount of salary Marko received is 2100 euros.

Note: If the student made a minor arithmetic error but has a good sequence of equations, deduct 1 point.