## Task 2 - 280732

In a factory for the production of alcoholic essences, a remaining stock of $300 \mathrm{~kg}$ of 32% alcohol is to be converted into a new stock of 40% alcohol by adding 90% alcohol.

Determine the amount of 90% alcohol needed to achieve this!
The remaining stock contains $\frac{32}{100} \cdot 300 \mathrm{~kg}=96 \mathrm{~kg}$ of alcohol. If one adds ( $x \mathrm{~kg}$ of 90 percent alcohol, and thus) $\frac{9}{10} x \mathrm{~kg}$ of alcohol, the new stock will contain $\left(96+\frac{9}{10} x\right) \mathrm{kg}$ of alcohol.

For this to be 40 percent of the amount $(300+x) \mathrm{~kg}$ of the new stock, the following must hold:

$$
96+\frac{9}{10} x=\frac{4}{10}(300+x)
$$

This leads to

$$
96+\frac{9}{10} x=120+\frac{4}{10} x \quad \Rightarrow \quad x=48
$$

The required amount of 90 percent alcohol is $48 \mathrm{~kg}$.