2 boys and 3 girls went on a trip. Both the boys and the girls carried equally weighted backpacks, and the 5 backpacks together weighed 44 $\mathrm{kg}$. On the way - so that 1 girl could always rest - the boys carried the girls' backpacks, one each on their backs and one together, in their hands, while the girls took the boys' backpacks on their backs, one each. Thus, except for the resting girl, everyone's load increased by the same amount. How much did each boy's and girl's backpack weigh?
The weight of the girl's backpack is evenly distributed among the other four hikers. Among them, the girls carry more by the amount that the boys' backpacks are heavier, so each boy's backpack is $1/4$ part heavier than the girls'. Thus, the total weight of the 5 backpacks is 5 and a half times the weight of a girl's backpack, which means a girl's backpack weighs $44: 5.5=8 \text{ kg}$, and a boy's is $1/4$ part more: $10 \text{ kg}$.

Indeed, this way, for 1 boy, $3 \cdot 8: 2=12 \text{ kg}$ is carried, which is $2 \text{ kg}$ more than his own backpack.

Huhn Ágnes (Szeged, Rókusi Ált. Isk. VIII. o. t.)