9.1. Winnie-the-Pooh and Piglet divided a cake between themselves. Piglet cried that he got too little. Then Pooh gave him a third of his share. This tripled the amount of cake Piglet had. What part of the cake did Pooh have initially, and what part did Piglet have?
Answer: Winnie-the-Pooh and Piglet originally had $6 / 7$ and $1 / 7$ of the cake respectively.

Let $a$ and $b$ be the shares of the cake for Winnie-the-Pooh and Piglet, respectively. Then $a+b=1$. From the condition $a / 3+b=3 b$, it follows that $a=6 b, 7 b=1, b=1 / 7$ and $a=6 / 7$.