1st drug

The first drug pack has an active ingredient ratio of L1: L2 = 2:1
The second drug pack has a ratio of active ingredients L1: L2 = 1:3

Which ratio do we have to mix the two packages so that the ratio of substances L1: L2 = 1:2?

Correct answer:

r =  1:4

Step-by-step explanation:

$$\begin{gathered} L_1=x\cdot (2/(2+1))+y\cdot (1/(1+3)) \\ {L}_2=x\cdot (1/(2+1)+y\cdot 3/(1+3) \\ \frac{2}{3}x+\frac{1}{4}y=\frac{1}{2}\cdot (\frac{1}{3}x+\frac{3}{4}y) \\ r=x/y \\ \frac{2}{3}r+\frac{1}{4}=\frac{1}{2}\cdot (\frac{1}{3}r+\frac{3}{4}) \\ 2/3\cdot r+1/4=1/2\cdot (r/3+3/4) \\ 6r=1.5 \\ r=\frac{1.5}{6}=0.25 \\ r=\frac{1}{4}=0.25=1:4 \end{gathered}$$

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