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Solution X, which is 50% alcohol, is combined with solution Y, which

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Solution X, which is 50% alcohol, is combined with solution Y, which [#permalink]

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Solution X, which is 50% alcohol, is combined with solution Y, which is 30% alcohol, to form 16 liters of a new solution that is 35% alcohol. How much of solution Y is used?

A. 4 liters
B. 6 liters
C. 8 liters
D. 10 liters
E. 12 liters
[Reveal] Spoiler: OA

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Re: Solution X, which is 50% alcohol, is combined with solution Y, which [#permalink]

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New post 11 Apr 2018, 00:42
You are given :
Y------------Mix-------------X
30%----------35%------------50%

Therefore the proportion of Y:X is 3:1.

For every 4 liters of mixture you have 3 liters of Y and 1 liter of X.
In total you have 16 liters, which means that you have : 3x4 = 12 liters of Y and 4 liters of X.

Therefore the answer is E : 12 Liters
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Solution X, which is 50% alcohol, is combined with solution Y, which [#permalink]

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New post 11 Apr 2018, 08:48
Bunuel wrote:
Solution X, which is 50% alcohol, is combined with solution Y, which is 30% alcohol, to form 16 liters of a new solution that is 35% alcohol. How much of solution Y is used?

A. 4 liters
B. 6 liters
C. 8 liters
D. 10 liters
E. 12 liters


let y=amount of solution Y used
.5(16-y)+.3y=.35*16
y=12 liters
E
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Solution X, which is 50% alcohol, is combined with solution Y, which [#permalink]

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New post 11 Apr 2018, 09:08
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Bunuel wrote:
Solution X, which is 50% alcohol, is combined with solution Y, which is 30% alcohol, to form 16 liters of a new solution that is 35% alcohol. How much of solution Y is used?

A. 4 liters
B. 6 liters
C. 8 liters
D. 10 liters
E. 12 liters

This weighted average formula is easy to use:

(% X)(Vol X) + (% Y)(Vol Y) = (% of X+Y)(Vol X+Y)

Solution X = 50 percent alcohol = .50
Solution Y = .30 alcohol
Total volume of resultant solution: 16 = X+Y
Let Y's volume = \(y\)
X's volume = \(16 -
y\)


\(.50(16 - y) + .30(y) = .35(16)\)
\(8 - .50y + .30y = 5.6\)
\(-.20y = -2.4\)
\(y = \frac{-2.4}{-.2}= 12\)
liters

Answer E
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Re: Solution X, which is 50% alcohol, is combined with solution Y, which [#permalink]

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New post 13 Apr 2018, 03:42
Bunuel wrote:
Solution X, which is 50% alcohol, is combined with solution Y, which is 30% alcohol, to form 16 liters of a new solution that is 35% alcohol. How much of solution Y is used?

A. 4 liters
B. 6 liters
C. 8 liters
D. 10 liters
E. 12 liters


Let,
x = amount solution X mixed
y = amount solution Y mixed
x+y = 16.........(A)

Using "Amount = concentration * volume " and the data given we get following eqn:

50x + 30y = 35 (x+y)

Solving this eqn we get: y=3x ...........(B)

With help of eqn (A) and (B) we get y = 12 (Option E)
Re: Solution X, which is 50% alcohol, is combined with solution Y, which   [#permalink] 13 Apr 2018, 03:42
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