6 ounces of water are mixed with X ounces of 40% alcohol vodka to

Question

6 ounces of water are mixed with X ounces of 40% alcohol vodka to create a 10% alcohol drink. What is X?

A) 1
B) 2
C) 6
D) 12
E) 18

Teeter Totter Method for Weighted Averages: Basic Example #4

GMATCoachBen · Answer

https://www.youtube.com/watch?v=uMCnXegM6lM
 ​​​​​​​
 Example 1 here, along with the solution below it, go into more detail on this Teeter Totter method.

Example 2 here

Example 3 here

sephiroth123 · Answer

I'm not too familiar with the teeter totter method, so decided to do it this way. Let me know if this method is acceptable?

The amount of alcohol will be the same, so X amount of the 40% vodka will be equal to 10% alcohol amount of the total mixture.

0.4X = 0.1 (6 + X)
0.4X = 0.6 + 0.1X
0.3X = 0.6
X = 2

Answer B; 2

GMATCoachBen · Answer

Yes, this works.

I encourage learning the teeter totter because the concept can be quite helpful and save a lot of time, especially on DS, and we've seen more mixture DS problems recently on the Focus Edition practice tests.

sephiroth123 · Answer

Great! Thanks for the insight!

Dbrunik · Answer

i just want to add that i think this is far easier to solve if you just think in terms of the final mixture 1/10 = alcohol/total volume.

0 alcohol in water + 2/5x = alcohol in final mixture

6 liters water plus some value x of the 40% alcohol.

((0+2/5x)/6+x)=1/10

cross multiply

3x=6

x=2

sarthak1701 · Answer

(0.4x/x+6) should equal 1/10 because x is 40% alcohol but in the combined drink of water and alcohol, only 10% is alcohol)

Let's look at the options:

X = 1, 0.4*1/7, not equal to 1/10

X = 2, 0.4*2/8 = 0.8/8 = 1/10, This satisfies our equation. Ans. B

LJRijn · Answer

We can use the weighted average method for this one which I start to love.
6 ounces of water are mixed with X ounces of 40% alcohol vodka to create a 10% alcohol drink. What is X?

To start we say 40% alcohol + 6 ounces of water result in a 10% alcoholic drink.
We can find the weighted average by \(\frac{(40%-10%)}{(10% - 0%)}\)
as we only add water so yea no alcohol. This gives us the ratio of the two drinks which then be \frac{30}{10}
or 3/1 for which we can also say that for 3 ounces of water for 1ounces of 40% alcohol
so we have 6 ounces of water and 2 ounces of wodka!
Which gives us B

If this is wrong ill gladly delete my answer! I hope it helps.
Link to the mixture theory
https://gmatclub.com/forum/weighted-ave ... l#p1586082

6 ounces of water are mixed with X ounces of 40% alcohol vodka to

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6 ounces of water are mixed with X ounces of 40% alcohol vodka to

Prep Toolkit

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