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

Question

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

olito · Answer

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

gracie · Answer

let y=amount of solution Y used
.5(16-y)+.3y=.35*16
y=12 liters
E

generis · Answer

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

shahsuhailp · Answer

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)

BrentGMATPrepNow · Answer

When solving mixture questions, I find it useful to sketch the solutions with the ingredients SEPARATED: 
 https://i.imgur.com/X6UPop8.png

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: 
 https://i.imgur.com/0etrR9M.png

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:
 https://i.imgur.com/2WJdtn9.png

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

Answer: E

RELATED VIDEO FROM OUR COURSE
 https://www.youtube.com/watch?v=7Or9gzROsjQ

JeffTargetTestPrep · Answer

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

Answer: E

Parvezahmed2210 · Answer

I find this way simple and quick

X/Y= 30-35/ 35-50 
X/Y= -5/-15= 1/3
Y=3X

Now,
X+Y=16
X+3X= 16
4X=16
X=4
Y= 4*3=12
E is the answer.

Posted from my mobile device

Basshead · Answer

Y/X = 50-35 / 35-30 = 15 / 5 = 3/1

X + Y = 16
X + 3X = 16
4X = 16
X = 4
Y = 12

Answer is E.

Bambi2021 · Answer

Weighted average with scale method for me.

30 - 35 - 50

Distances from 35 are in ratio 1:3. Flip the ratio to get the proportions of solutions in the mixed solution. New ratio is 3:1. 0,75*16 = 12.

errorlogger · Answer

E!
 https://i.imgur.com/rB4Mpd4.jpg

Liberatehk1920 · Answer

X + Y = 16
X + 3X = 16
4X = 16
X = 4
Y = 12

bumpbot · Answer

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

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