## Task 2 - 060812

From cow's milk, $21 \%$ of the mass can be obtained as cream. From cream, butter is produced, and the mass of butter is $23 \%$ of the cream mass.

Determine the smallest amount of cow's milk that is sufficient to produce exactly $1 \mathrm{~kg}$ of butter under the given conditions!

The milk quantity should be given in kg and expressed as a decimal, rounded to one decimal place to ensure that the amount is sufficient to produce $1 \mathrm{~kg}$ of butter.
From $x \, \text{kg}$ of milk, one obtains $\frac{21}{100} x \, \text{kg}$ of cream and from that $\frac{23}{100} \cdot \frac{21}{100} x \, \text{kg}$ of butter.

From the equation $\frac{23 \cdot 21}{100 \cdot 100} x = 1$ it follows that $x = \frac{10000}{21 \cdot 23} = \frac{10000}{483}$.

Since $20.7 < \frac{10000}{483} < 20.8$, considering exactly one decimal place, $20.8 \, \text{kg}$ of milk is the smallest amount sufficient to produce $1 \, \text{kg}$ of butter using the specified method.