Pharmacist

The pharmacist had a 12 liters vessel herbal lotion, which contained a 30% active ingredient. Her assistant poured 18 liters of herbal lotion containing 45% of the active ingredient into a container. What percentage of herbal lotion was produced?

Correct answer:

p =  39 %

Step-by-step explanation:

$$\begin{gathered} V_1=12\text{l} \\ {p}_1=30\%=\frac{30}{100}=0.3 \\ {V}_2=18\text{l} \\ {p}_2=45\%=\frac{45}{100}=0.45 \\ p=100\cdot \frac{p_1\cdot V_1+p_2\cdot V_2}{V_1+V_2}=100\cdot \frac{\frac{3}{10}\cdot V_1+\frac{9}{20}\cdot V_2}{V_1+V_2}=100\cdot \frac{0.3\cdot 12+0.45\cdot 18}{12+18}=39\% \end{gathered}$$

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