A beauty

A beauty supply company has 53 liters of 5% hydrogen peroxide solution on hand and a nearly limitless amount of a solution containing 35% hydrogen peroxide. How many liters of the 35% hydrogen peroxide solution should the company add to the 5% hydrogen peroxide solution to obtain a mixture of 11% hydrogen peroxide?

Correct answer:

V₂ =  13.25 l

Step-by-step explanation:

$$\begin{gathered} V_1=53\text{l} \\ {q}_1=5\%=\frac{5}{100}=\frac{1}{20}=0.05 \\ {q}_2=35\%=\frac{35}{100}=\frac{7}{20}=0.35 \\ q=11\%=\frac{11}{100}=0.11 \\ {V}_1\cdot q_1+V_2\cdot q_2=q\cdot (V_1+V_2) \\ 53\cdot 0.05+V_2\cdot 0.35=0.11\cdot (53+V_2) \\ 0.24V_2=3.18 \\ {V}_2=\frac{3.18}{0.24}=13.25 \\ {V}_2=\frac{53}{4}=13.25=13.25\text{l} \end{gathered}$$

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