Three girlfriends met at a cottage and went mushroom picking. They found a total of 55 mushrooms. Upon returning, they made a fried mushroom dish, divided it into four equal portions, and invited their friend Pepa to join them. Líba contributed six of her mushrooms to the dish, Maruška eight, and Sárka five. Each then had the same number of mushrooms left. Pepa gave them a box of chocolates, containing 38 chocolates, and said they should fairly divide them according to how much they contributed to his meal.

1. How many mushrooms did each find?
2. How should they divide the chocolates according to Pepa?

(M. Volfová)
1. The friends contributed a total of $6+8+5=19$ mushrooms to the fried dish, so they had $55-19$ = 36 left. They then divided the remaining mushrooms equally, so each of them had $36: 3=12$ mushrooms. Líba contributed 6 mushrooms to the dish, so she must have found $12+6=18$ mushrooms. Maruška contributed 8, so she must have found $12+8=20$ mushrooms, and Šárka contributed 5, so she must have found $12+5=17$ mushrooms.

2. Each of them ate a quarter of the fried dish, meaning each ate $\frac{19}{4}=4 \frac{3}{4}$ mushrooms. Líba contributed 6 mushrooms to the dish (she ate $4 \frac{3}{4}$ herself), so she contributed $6-4 \frac{3}{4}=1 \frac{1}{4}$, or $\frac{5}{4}$, mushrooms to Pepa's portion. Maruška contributed 8 mushrooms, so she contributed $8-4 \frac{3}{4}=3 \frac{1}{4}=\frac{13}{4}$ mushrooms to Pepa's portion. Šárka contributed 5 mushrooms, so she contributed $5-4 \frac{3}{4}=\frac{1}{4}$ mushrooms to Pepa's portion.

According to Pepa, the girls should divide the candies in the ratio $\frac{5}{4}: \frac{13}{4}: \frac{1}{4}$. This is the same as the ratio $5: 13: 1$ or $10: 26: 2$, which totals 38 parts, corresponding to the 38 candies in the candy box. Líba should get 10 candies, Maruška 26, and Šárka 2.