Three glasses

Three glasses of different colors have different volumes. Red 1.5 liter is filled from 2/5, blue 3/4 liter is filled from 1/3, and the third green 1.2 liter is empty. Pour green glass 1/4 of the contents from the red glass and 2/5 of the content from the blue one. Express a fraction of how much the green glass is filled with.

Result

z =  0.208

Solution:

C=1.5 l M=3/4=34=0.75 l Z=1.2 l  V=C 25 14+M 13 25=1.5 25 14+0.75 13 25=14=0.25 l  z=VZ=0.251.2=5240.2083=0.208C = 1.5 \ l \ \\ M = 3/4 = \frac{ 3 }{ 4 } = 0.75 \ l \ \\ Z = 1.2 \ l \ \\ \ \\ V = C \cdot \ \frac{ 2 }{ 5 } \cdot \ \frac{ 1 }{ 4 } + M \cdot \ \frac{ 1 }{ 3 } \cdot \ \frac{ 2 }{ 5 } = 1.5 \cdot \ \frac{ 2 }{ 5 } \cdot \ \frac{ 1 }{ 4 } + 0.75 \cdot \ \frac{ 1 }{ 3 } \cdot \ \frac{ 2 }{ 5 } = \frac{ 1 }{ 4 } = 0.25 \ l \ \\ \ \\ z = \frac{ V }{ Z } = \frac{ 0.25 }{ 1.2 } = \frac{ 5 }{ 24 } \doteq 0.2083 = 0.208







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