Laboratory

In a laboratory, twelve litres of 80% alcohol were to be diluted to produce 40% alcohol, and then further combined to make a final 70% alcohol solution. A five-litre barrel of 40% alcohol was available. How much of the 40% alcohol will remain in the barrel?

Final Answer:

x =  1 l

Step-by-step explanation:

$$\begin{gathered} V_1=12\text{l} \\ {r}_1=80\%=\frac{80}{100}=\frac{4}{5}=0.8 \\ {r}_2=40\%=\frac{40}{100}=\frac{2}{5}=0.4 \\ {r}_3=70\%=\frac{70}{100}=\frac{7}{10}=0.7 \\ {V}_2=5\text{l} \\ {r}_1\cdot V_1+r_2\cdot w=r_3\cdot (V_1+w) \\ 0.8\cdot 12+0.4\cdot w=0.7\cdot (12+w) \\ 0.3w=1.2 \\ w=\frac{1.2}{0.3}=4 \\ w=4 \\ x=V_2-w=5-4=1\text{l} \end{gathered}$$

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