Solution mixtures

We have 1 liter of 80% solution. Every hour, pour 1 dl of the solution, add 1 dl of water (a 0% solution), and mix. What percent solution will we have after two mixings?

Correct answer:

p₂ =  64.8 %

Step-by-step explanation:

$$\begin{gathered} p_0=80\%=\frac{80}{100}=\frac{4}{5}=0.8 \\ {V}_0=1\cdot 10=10\text{dl} \\ w=1\text{dl} \\ {V}_1=p_0\cdot (V_0-w)=0.8\cdot (10-1)=\frac{36}{5}=7.2\text{dl} \\ {p}_1=\frac{V_1}{V_0}=\frac{7.2}{10}=\frac{18}{25}=0.72 \\ {V}_2=p_1\cdot (V_0-w)=0.72\cdot (10-1)=\frac{162}{25}=6.48\text{dl} \\ {p}_2=100\cdot \frac{V_2}{V_0}=100\cdot \frac{6.48}{10}=64.8\% \end{gathered}$$

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