In Miroslav's kingdom, the cobbler Matěj used to go not only to sing but also to eat and drink well. For one gold piece, he got a whole goose and one jug of wine. Then, however, they increased the prices by $20 \%$, and for a gold piece, he got only half a jug of wine and a whole goose. It is said that after the full moon, prices will rise again by $20 \%$. Will Matěj then get at least one whole goose for his gold piece?

(Volfová)
Let the price of the whole goose be denoted as $h$, and the price of a jug of wine as $v$.

a) Situation before the price increase: $h+v=1$.

b) Situation after the price increase of $20\%: h+v=1.2$.

At the same time, we know that $h+\frac{v}{2}=1$, so $\frac{v}{2}=0.2$, which means the price of a jug of wine after the price increase was $v=0.4$ gold coins, and the price of the whole goose was $h=0.8$ gold coins.

c) Situation after the assumed additional $20\%$ price increase: $h=1.2 \cdot 0.8=0.96$ gold coins, so even after the additional price increase, Matej would still get a whole goose for one gold coin.