1. Janez spent $\frac{3}{5}$ of the money he had, then $\frac{5}{9}$ of the remainder, and finally $\frac{3}{8}$ of the new remainder. He was left with 80 euros. How much money did he have at the beginning?
1. Let $x$ be the initial amount. We calculate the share of money that Janez has after the first expense, which is $\frac{2}{5} x$. Then we calculate the new share of money that Janez has after the second expense, which is $\frac{8}{45} x$. After the third expense, Janez has $\frac{1}{9} x$ left. We set up the equation $\frac{1}{9} x=80$. We calculate the desired amount to be 720 euros.

Setting up the first equation and simplifying $x-\frac{3}{5} x=\frac{2}{5} x \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots$ point

Setting up the second equation and simplifying $\frac{2}{5} x-\frac{5}{9} \cdot \frac{2}{5} x=\frac{8}{45} x \ldots \ldots \ldots \ldots \ldots \ldots \ldots . \ldots$ point

Setting up the third equation and simplifying $\frac{8}{45} x-\frac{3}{8} \cdot \frac{8}{45} x=\frac{1}{9} x \ldots \ldots \ldots \ldots \ldots \ldots \ldots . \ldots$ point

![](https://cdn.mathpix.com/cropped/2024_06_07_2b0bf3255e176946d93cg-06.jpg?height=60&width=1639&top_left_y=1900&top_left_x=206)

![](https://cdn.mathpix.com/cropped/2024_06_07_2b0bf3255e176946d93cg-06.jpg?height=46&width=1636&top_left_y=1956&top_left_x=210)

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