Milk with water 2

If 50 liters of a mixture contains milk and water in a ratio of 3:2, how much milk must be added to the mixture to have milk and water in a ratio of 9:4?

Final Answer:

m =  15 l

Step-by-step explanation:

$$\begin{gathered} V=50\text{l} \\ {r}_1=3:2=1.5 \\ {r}_2=9:4=2.25 \\ x:(V-x)=r_1 \\ x=r_1\cdot (V-x) \\ x=1.5\cdot (50-x) \\ 2.5x=75 \\ x=\frac{75}{2.5}=30 \\ x=30 \\ (x+m):(V-x)=r_2 \\ (x+m)=r_2\cdot (V-x) \\ (30+m)=2.25\cdot (50-30) \\ m=15=15\text{l} \end{gathered}$$

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