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

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

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

Answer: E

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

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)

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

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.

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.

E!

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

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