Problem 878

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

!

!

Answer . .............................................................................................................