Grandma made a soup for her 5 grandchildren to share equally. Angela and Daniela arrived, divided the soup equally into 5 bowls, each took their share, returned the leftovers to the pot to keep it warm, and went to play in the park. Laura, when she arrived, thought she was the first and divided the soup into 5 equal bowls, took one of them, and returned the rest to the pot. João, when he arrived, thought only Laura had taken her share, divided it into 4 bowls, took his share, and went to sleep. When Toni arrived, knowing he was the last, he took all the remaining soup.

a) What fraction of the soup did Laura drink?

b) Who drank the most soup?

c) If the soup were divided into 100 ml containers, everyone would have drunk an integer number of containers. What is the smallest possible amount of soup that was in the pot?

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Solution

a) Ângela and Daniela each took $\frac{1}{5}$, leaving $\frac{3}{5}$ of the soup in the pot. Laura divided the remaining $\frac{3}{5}$ into 5 parts, taking 1 part, which is $\frac{1}{5} \cdot \frac{3}{5}=\frac{3}{25}$.

b) Continuing from the previous item, after Laura's turn, $\frac{3}{5}-\frac{3}{25}=\frac{15-3}{25}=\frac{12}{25}$ of the soup remained. João divided this fraction into 4 parts, so he took $\frac{1}{4} \cdot \frac{12}{25}=\frac{3}{25}$, leaving $\frac{12}{25}-\frac{3}{25}=\frac{9}{25}$, which is the fraction that Toni took. Therefore, Toni was the one who took the most soup.

c) There would be 25 bowls, or 2.5 liters.