Problem 7.1. Andrei, Boris, and Denis were eating candies, each at their own constant rate. While Andrei ate 4 candies, Boris managed to eat only 3. Denis ate the fastest: he ate 7 candies while Andrei ate 6. In total, the boys ate 70 candies. How many candies did each of them eat?
Answer: Andrey ate 24, Boris ate 18, Denis ate 28.

Solution. From the condition, it follows that while Andrey eats 12 candies, Boris eats 9 candies, and Denis eats 14, i.e., together they eat 35 candies. Then, to eat 70 candies, each of them should eat twice as much: Andrey - 24, Boris - 18, Denis - 28.