This problem is about rations and proportions .
Problem A jar of full wine, extracted quarter(1/4) replacing it with water. A second chance in the third part(1/3) of the content is extracted replacing it with water. In a third and last chance is reextracted fifth(1/5) replacing it with water. That proportion is in the end the wine and water ?
Thanks!
Subtract 1/4 from 1
1-(1/4) which gives 3/4 wine left
3/4 + x =1, solve for x to find the water you need to add
3/4 wine + 1/4 water = 1
Remove 1/3 from the jar.
The amount that you remove is based on how much wine and water you have so they are weighted differently.
[(3/4)-(3/4)(1/3)] wine + [(1/4)-(1/4)(1/3)] water + x = 1
Again solve for x to find the amount of water that is needed to add back in.
The value is x = 1/3
(1/2) wine + (1/2) water = 1
Now remove the 1/5 of the liquid in the jar.
[(1/2)-(1/2)(1/5)] wine + [(1/2)-(1/2)(1/5)] water + x = 1
Solve for x gives, x=1/5
Add back in to get
(2/5) wine + (3/5) water = 1
These are the ratios.