Concentrate - juice

To produce one liter of 100% juice, 2 kg of fruit are needed. Juice is made by squeezing the fruit into a pulp, drying it, and obtaining a concentrate, which is then transported to the processing site where it is diluted again.

How many liters of fruit juice did we get if a total of 8 kg of fruit were used to produce 16% fruit juice?

Correct answer:

V =  25 l

Step-by-step explanation:

$$\begin{gathered} m_1=2\text{kg} \\ {V}_1=1\text{l} \\ {m}_2=8\text{kg} \\ {V}_2=V_1\cdot \frac{m_2}{m_1}=1\cdot \frac{8}{2}=\frac{1\cdot 8}{2}=\frac{8}{2}=4\text{l} \\ q=16\%=\frac{16}{100}=\frac{4}{25}=0.16 \\ q\cdot V=V_2 \\ V=V_2/q=4/\frac{4}{25}=4:\frac{4}{25}=4\cdot \frac{25}{4}=\frac{4\cdot 25}{4}=\frac{100}{4}=25\text{l} \end{gathered}$$

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