## Task 3 - 250613

Dirk and Jörg met at the secondary raw materials collection center. Jörg has bundled his waste paper into several packages of $5 \mathrm{~kg}$ each and also has an additional $3 \mathrm{~kg}$ of loose paper.

Dirk delivers $32 \mathrm{~kg}$ of paper. When they compare their collection results, they also realize that together they collected more than $50 \mathrm{~kg}$ of waste paper.

How many bundles of $5 \mathrm{~kg}$ can Jörg have delivered, given that we also know Dirk had more waste paper than Jörg?

List all possibilities!
Jörg has delivered less than (the 32 kg brought by Dirk). Because $50-32=18$, he has delivered more than $18 \mathrm{~kg}$. If he had brought three or fewer bundles of $5 \mathrm{~kg}$, he would have delivered only $18 \mathrm{~kg}$ or less due to $3 \cdot 5+3=18$.

If he had brought six or more bundles of $5 \mathrm{~kg}$, he would have delivered more than $32 \mathrm{~kg}$ due to $6 \cdot 5+3=33$. Therefore, he could only have brought four or five bundles of $5 \mathrm{~kg}$.

These two cases are indeed possible, as they result in $4 \cdot 5+3=23$ and $5 \cdot 5+3=28$, respectively.