1. Three travelers sat down to eat. The first one took out 3 loaves of bread, and the second one took out 4 loaves of bread. They divided the seven loaves into three equal parts and ate them. The third traveler took out 7 coins and said, "I had no bread, but here are 7 coins, and you should divide them fairly."

How many coins should the first and how many to the second traveler receive?
Solution. Each traveler took $\frac{7}{3}$ of the loaves. The third traveler paid his $\frac{7}{3}$ with 7 coins, meaning he paid 1 coin for each third of a loaf.

The first traveler brought 3 loaves, i.e., $\frac{9}{3}$, and took $\frac{7}{3}$, which means he gave $\frac{2}{3}$ to the third traveler. Similarly, the second traveler brought $\frac{12}{3}$, and took $\frac{7}{3}$, which means he gave $\frac{5}{3}$ of the loaves to the third traveler. Finally, the first traveler should receive 2 coins, and the second traveler should receive 5 coins.