## 1. Magic Drink

Petar and Tomo are playing a game that uses 3-crown and 5-crown coins. If they land on a golden field, they can buy a magic drink. Petar paid for the drink with 3-crown coins, while Tomo used 5-crown coins. What is the price of the magic drink if together they gave more than 60 but fewer than 70 coins?

## Result: 120
Solution: Since Petar paid for the drink with 3-kuna bills, and Tomo with 5-kuna bills, the price must be divisible by both 3 and 5, meaning it is divisible by 15. For every 15 kuna, Petar gave 5 of his bills, and Tomo gave 3 of his. This means the total number of bills is divisible by 8. Since they gave more than 60 but fewer than 70 bills, they paid with 64 bills.

Since Petar paid with 3-kuna bills and Tomo with 5-kuna bills, it is clear that Petar gave more bills than Tomo, so we look at cases where the number of bills Petar gave is greater than 32. If Petar gave 35 bills, Tomo gave 29, which is impossible because $35 \cdot 3 \neq 29 \cdot 5$.

If Petar gave 40 bills, Tomo gave 24, which is a solution because $40 \cdot 3 = 24 \cdot 5 = 120$.

Further increasing (or decreasing) the number of Petar's bills does not yield another solution, meaning the price of the magic drink is 120 kuna.