Problem 5. Vladо, Boban, and Kатe have a total of 600 denars. If Vladо spends half of his money, Boban spends two-thirds of his money, and Kатe spends four-fifths of her money, then each of them will have the same amount of money left. How much money did each of them have?
Solution. Let $x$ be the amount of money each of them has left after spending. Vlad spent half, so he initially had $2 x$. Boban spent two thirds, leaving him with one third, so he initially had $3 x$. One fifth of Katarina's money was left, meaning she initially had $5 x$. Together, they initially had 600 denars, so $2 x+3 x+5 x=600$, from which $x=60$ denars. Therefore, Vlad had 120 denars, Boban 180 denars, and Katarina 300 denars.

## V grade - nine-year-old