## Task 2 - 240812

Cathrin presents the following puzzle to her classmates in the "Mathematics" study group:

A bottle and a glass together weigh as much as a jug. The bottle alone weighs as much as the glass together with a plate, while three such plates together weigh as much as two such jugs. How many such glasses weigh as much as the bottle?
Let $F, G, K, T$ be the weights of the bottle, glass, jug, and plate, respectively, then

\[
\begin{aligned}
F+G & =K \\
F & =G+T \\
3 T & =2 K
\end{aligned}
\]

From (2) it follows that $3 F=3 G+3 T$. Substituting (3) into this, we get

\[
3 F=3 G+2 K
\]

From (1) it follows that $2 K=2 F+2 G$. Substituting this into (4), we obtain $3 F=3 G+2 F+2 G$ and thus $F=5 G$.

Therefore, five glasses weigh as much as the bottle.