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

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Math Expert
Joined: 02 Sep 2009
Posts: 58464
Solution X, which is 50% alcohol, is combined with solution Y, which  [#permalink]

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10 Apr 2018, 21:50
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80% (01:31) correct 20% (02:04) wrong based on 176 sessions

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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

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

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11 Apr 2018, 00:42
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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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Joined: 07 Dec 2014
Posts: 1224
Solution X, which is 50% alcohol, is combined with solution Y, which  [#permalink]

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11 Apr 2018, 08:48
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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

let y=amount of solution Y used
.5(16-y)+.3y=.35*16
y=12 liters
E
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Joined: 22 May 2016
Posts: 3581
Solution X, which is 50% alcohol, is combined with solution Y, which  [#permalink]

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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

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

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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)
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Joined: 12 Sep 2015
Posts: 4019
Re: Solution X, which is 50% alcohol, is combined with solution Y, which  [#permalink]

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28 Aug 2018, 12:06
Top Contributor
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

When solving mixture questions, I find it useful to sketch the solutions with the ingredients SEPARATED:

Since we want to determine the volume of solution Y needed, let's...
Let y = volume (in liters) of solution Y needed
This means 16 - y = volume (in liters) of solution X needed (since the combined volume of both amounts is 16 liters)

So, we get:

Now let's determine the volume of alcohol in each container.

Solution Y is 30% alcohol. We have y liters of solution Y.
So, the volume of alcohol = 0.3y

Solution X is 50% alcohol. We have 16 - y liters of solution X.
So, the volume of alcohol = 0.5(16 - y) = 8 - 0.5y

The combined solution is 35% alcohol. There are 16 liters of this solution.
So, the volume of alcohol = 0.35(16) = 5.6

So, our sketch looks like this:

At this point, we can focus on the volume of alcohol in each container.
We know that: (volume of alcohol in 1st container) + (volume of alcohol in 2nd container) = volume of alcohol in combined solution.
In other words: 0.3y + (8 - 0.5y) = 5.6
Simplify: 8 - 0.2y = 5.6
Subtract 8 from both sides to get: -0.2y = -2.4
Solve: y = 12

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

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30 Aug 2018, 17:57
1
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

We start with x liters of a solution that is 50% alcohol. We add to it y liters of a solution that is 30% alcohol. The result is (x + y) liters of a solution that is 35% alcohol. We can create the equations:

0.5x + 0.3y = 0.35(x + y)

50x + 30y = 35x + 35y

15x = 5y

3x = y

and

x + y = 16

Substituting, we have:

x + 3x = 16

4x = 16

x = 4, so y = 12

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Re: Solution X, which is 50% alcohol, is combined with solution Y, which   [#permalink] 30 Aug 2018, 17:57
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