1.2. A ballpoint pen costs 10 rubles, a gel pen costs 40 rubles, and a fountain pen costs 60 rubles. What is the maximum number of ballpoint pens that can be bought if you need to buy exactly 15 pens in total, and among them there must be pens of all three types, and you need to spend exactly 500 rubles?
Answer: 6. Comments. The solutions are two triples of integers $(6,5,4)$ and $(4,10,1)$.