7. In a bus without a conductor, there were 20 people. Although they only had coins worth 10, 15, and 20 kopecks, each of them paid for the fare and received the change they were due. How could this have happened? Prove that they had no fewer than 25 coins. (One ticket costs 5 kopecks.)
7. Let's first prove that the passengers had no less than 25 coins. Indeed, each passenger should receive change, i.e., no fewer than twenty coins should remain in the hands of the passengers. One ruble was dropped into the cash box, so there must be no fewer than five coins (since the largest coin available is 20 kopecks).

Now let's show that the situation described in the problem could have happened. Indeed, there could have been five groups of four people in the bus, and in each group, one person had two ten-kopeck coins, two people had one fifteen-kopeck coin each, and one person had a twenty-kopeck coin. The first person gave 10 kopecks to the second and third persons and took 15 kopecks from the second person. The third person gave his 15 kopecks to the fourth person, and the fourth person dropped his 20 kopecks into the cash box.