The value of [tex]x+y[/tex] is 237 liters.
Given information:
A 63 liter mixture contains milk and water in a ratio of 4:5.
Let the initial amount of water be a. So, the amount of milk will be [tex]63-a[/tex].
The initial mixture can be written as,
[tex]\dfrac{63-a}{a}=\dfrac{4}{5}[/tex]
The initial amount of water and milk will be,
[tex]\dfrac{63-a}{a}=\dfrac{4}{5}\\315-5a=4a\\9a=315\\a=35\\63-a=28[/tex]
x liters of milk and y liters of water are added to the mixture, resulting in a milk to water ratio of 7:5.
The mixture, now, can be written as,
[tex]\dfrac{28+x}{35+y}=\dfrac{7}{5}\\140+5x=245+7y[/tex]
60 liters of the mixture are drained and replaced with 60 liters of water, resulting in a milk to water ratio of 7:8.
Draining will release the amount of water and milk in the ratio 7:5 which is its concentration. So, 35 liters of milk and 25 liters of water will be drained.
The final mixture can be written as,
[tex]\dfrac{28+x-35}{35+y-25+60}=\dfrac{7}{8}\\\dfrac{x-7}{y+70}=\dfrac{7}{8}\\8x-56=7y+490[/tex]
Solve for x and y as,
[tex]140+5x=245+7y\\8x-56=7y+490\\3x-196=245\\x=147\\y=90[/tex]
So, the value of [tex]x+y[/tex] will be,
[tex]x+y=147+90\\=237[/tex]
Therefore, the value of [tex]x+y[/tex] is 237 liters.
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https://brainly.com/question/11897796
