João, Jorge, José, and Jânio are good friends. Once, João was out of money, but his friends had some. So Jorge gave João one fifth of his money, José gave one fourth of his money, and Jânio gave one third of his money. If they all gave the same amount of money to João, what fraction of the group's money did João end up with?
If $A$ is the amount of money João received from each of his friends, then he received a total of $3 A$. Since he received, from Jorge, one fifth of his money, then Jorge had $5 A$. Similarly, José had $4 A$ and Jânio had $3 A$. Thus, the three friends had, together, $5 A+4 A+3 A=12 A$ and the fraction of the group's money that João ended up with was $(3 \mathrm{~A}) /(12 \mathrm{~A})=1 / 4$, that is, one fourth.