Problem 6.3. Three merchants: Foma, Yerema, and Julius met in Novgorod. If Foma gives Yerema 70 gold coins, then Yerema and Julius will have the same amount of money. If Foma gives Yerema 40 gold coins, then Foma and Julius will have the same amount of money. How many gold coins should Foma give Yerema so that they both have the same amount of money?
Answer: 55.

Solution. From the first condition, it follows that Yuliy has 70 more coins than Yeremy. From the second condition, it follows that Foma has 40 more coins than Yuliy. Therefore, Foma has $40+70=110$ more coins than Yeremy. For them to have an equal amount of money, Foma must give Yeremy half of this difference, which is $\frac{110}{2}=55$ coins.