Question 423344: if water is added in 80% wine then the wine become 60% . find the ratio of water is added to the wine
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! your mixture is currently 80% wine.
that means it is 20% water.
let w equal the amount of water in the mixture.
let m = the amount of mixture.
currently w = .2 * m
that means the mixture is 20% water and 80% wine.
let y be equal to the amount of water you want to add to the mixture to make it 60% wine.
60% wine means 40% water.
your new formula will be:
(x + y) = .4 * (m + y)
since we know that x = .2 * m, we can substitute in this equation to get:
(.2 * m + y = .4 * (m + y)
removing parentheses, we get:
.2 * m + y = .4 * m + .4 * y
subtract .4 * y from both sides of this equation and subtract .2 * m from both sides of this equation to get:
y - (.4 * y) = (.4 * m) - (.2 * m)
simplify to get:
.6 * y = .2 * m
divide both sides of this equation by .6 to get:
y = (.2/.6) * m
simplify to get:
y = .33333333 * m
in our equation of x + y = .4 * (m + y), we can substitute for x and y to get:
(.2 * m + .33333333 * m = .4 * (m + .333333333 * m)
simplify to get:
.533333333333 * m = 1.33333333333 * m
the .53333333333 * m is the amount of water in the new mixture.
that represents .53333333333333 / 1.333333333333 * m which is equal to .4 * m which is the exact mixture that we want.
you start with x = .2 * m
you add y = .33333333333 * m.
The amount of water that is added to the original mixture is equal to 1/3 of the original mixture.
assume your original mixture was 12 gallons of water and 48 gallons of wine.
that's a total of 60 gallons of which 20% is water and 80% is wine.
you want to add 1/3 gallons * 60 of water to the mixture.
that's an additional 20 gallons of water.
the amount of water is now 32 gallons of water and the amount of wine is still 48 gallons for a total of 80 gallons of mixture.
32 / 80 = .4 = 40% of the mixture is water.
48 / 80 = .6 = 60% of the mixture is wine.
your answer is:
you add water equal to 1/3 of the original mixture to get 40% water and 60% wine in the new mixture.
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