Juice water mixture

The drink was mixed from one hundred percent juice and water in a ratio of 1.5 liters of juice to 2.5 liters of water. Calculate how many liters of this drink will be created by mixing 1 liter of water and juice in the corresponding ratio. Calculate how many liters of juice are needed to make 100 liters of this drink.

Final Answer:

V =  1.6 l
V₅ =  37.5 l

Step-by-step explanation:

$$\begin{gathered} V_1=1.5\text{l} \\ {V}_2=2.5\text{l} \\ r=V_1:V_2=1.5:2.5=15:25=3:5 \\ {V}_3=1\text{l} \\ {V}_3:V_4=5:3 \\ {V}_4=V_3\cdot \frac{3}{5}=1\cdot \frac{3}{5}=\frac{1\cdot 3}{5}=\frac{3}{5}=0.6\text{l} \\ V=V_3+V_4=1+\frac{3}{5}=\frac{1\cdot 5}{5}+\frac{3}{5}=\frac{5}{5}+\frac{3}{5}=\frac{5+3}{5}=\frac{8}{5}=\frac{8}{5}\text{l}=1.6\text{l} \end{gathered}$$

$$\begin{gathered} V_6=100\text{l} \\ {V}_5=\frac{3}{3+5}\cdot V_6=\frac{3}{3+5}\cdot 100=\frac{75}{2}\text{l}=37.5\text{l} \end{gathered}$$

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