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:

$C=1.5 \ \text{l} \ \\ M=3/4=\dfrac{ 3 }{ 4 }=0.75 \ \text{l} \ \\ Z=1.2 \ \text{l} \ \\ \ \\ V=C \cdot \ \dfrac{ 2 }{ 5 } \cdot \ \dfrac{ 1 }{ 4 } + M \cdot \ \dfrac{ 1 }{ 3 } \cdot \ \dfrac{ 2 }{ 5 }=1.5 \cdot \ \dfrac{ 2 }{ 5 } \cdot \ \dfrac{ 1 }{ 4 } + 0.75 \cdot \ \dfrac{ 1 }{ 3 } \cdot \ \dfrac{ 2 }{ 5 }=\dfrac{ 1 }{ 4 }=0.25 \ \text{l} \ \\ \ \\ z=\dfrac{ V }{ Z }=\dfrac{ 0.25 }{ 1.2 } \doteq \dfrac{ 5 }{ 24 } \doteq 0.2083 \doteq 0.208$

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