Task 1. From 3 deciliters of cough syrup, which contained $10 \%$ distilled water, the pharmacist prepared a syrup for a child, which was supposed to contain $40 \%$ water. How many deciliters of water did she add to the three deciliters of syrup?
Solution. Let $x$ denote the amount of water (expressed in deciliters) that the pharmacist added to the three deciliters of syrup. Then, according to the conditions in the problem, we get the equation $\frac{10}{100} \cdot 3 + x = \frac{40}{100}(3 + x)$. This is equivalent to $3 + 10x = 12 + 4x, 6x = 9$, and from there $x = 1.5 dl$.