BTG flashcards problem

How many liters of a solution that is 10% alcohol by volume must be added to 2 liters of a solution that is 50% alcohol by volume to create a solution that is 15% alcohol by volume?
A) 10
B) 12
C) 14
D) 16
E) 18

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

Start with 2 liters of solution that is 50% alcohol:

When we draw this with the ingredients separated, we see we have 1 liter of alcohol in the mixture.


Next, we'll let x = the number of liters of 10% solution we need to add.
Since 10% of the mixture is alcohol, we know that 0.1x = the volume of alcohol in this solution:


At this point, we can add the two solutions to get the following volumes:


Since the resulting solution is 15% alcohol (i.e., 15/100 of the solution is alcohol), we can write the following equation:
(1 + 0.1x)/(2 + x) = 15/100
Simplify to get: (1 + 0.1x)/(2 + x) = 3/20
Cross multiply to get: 20(1 + 0.1x) = 3(2 + x)
Expand: 20 + 2x = 6 + 3x
Rearrange/solve: 14 = x

Answer: C

Cheers,
Brent

Here are some additional mixture questions to practice with:
https://www.beatthegmat.com/liters-of-mi ... 71387.html
https://www.beatthegmat.com/percentage-m ... 68631.html
https://www.beatthegmat.com/rodrick-mixe ... 70387.html
https://www.beatthegmat.com/mixure-probl ... 61767.html
https://www.beatthegmat.com/mixture-rati ... 91643.html