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BTG flashcards problem

This topic has 2 expert replies and 0 member replies
sparkles3144 Master | Next Rank: 500 Posts Default Avatar
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BTG flashcards problem

Post Sun Jun 15, 2014 1:09 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    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?

    Answer 14

    I disagree with the answer.
    Can someone show steps?

    Thanks!

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    Post Sun Jun 15, 2014 2:02 am
    Quote:
    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
    We can use ALLIGATION -- a great way to handle MIXTURE PROBLEMS.

    Let X = the 10% solution and Y = the 50% solution.

    Step 1: Plot the 3 percentages on a number line, with the percentages for X and Y on the ends and the percentage for the mixture in the middle.
    X 10------------15------------50 Y

    Step 2: Calculate the distances between the percentages.
    X 10-----5-----15-----35-----50 Y

    Step 3: Determine the ratio in the mixture.
    The required ratio of X to Y is equal to the RECIPROCAL of the distances in red.
    X:Y = 35:5 = 7:1.

    Since X:Y = 7:1 = 14:2, 14 liters of X must be added to 2 liters of Y.

    The correct answer is C.

    An alternate approach is to PLUG IN THE ANSWERS, which represent the amount of 10% solution that must be added to 2 liters of 50% solution.

    Answer choice C: 14 liters
    Amount of alcohol in 14 liters of 10% solution = 10% of 14 = 1.4 liters.
    Amount of alcohol in 2 liters of 50% solution = 50% of 2 = 1 liter.
    (total alcohol)/(total volume) = (1.4 + 1)/(14 + 2) = (2.4)/16 = 24/160 = 3/20 = 15/100 = 15%.
    Success!

    The correct answer is C.

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    Post Sun Jun 15, 2014 5:06 am
    Quote:
    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:
    ttp://postimg.org/image/vnr9nojgt/" target="_blank">
    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:
    ttp://postimg.org/image/b4wdim5jh/" target="_blank">

    At this point, we can add the two solutions to get the following volumes:
    ttp://postimg.org/image/5urerblal/" target="_blank">

    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:
    http://www.beatthegmat.com/liters-of-mixture-x-in-the-50-mixture-t271387.html
    http://www.beatthegmat.com/percentage-mixture-t268631.html
    http://www.beatthegmat.com/rodrick-mixes-a-martini-that-has-a-volume-of-n-ounces-havi-t270387.html
    http://www.beatthegmat.com/mixure-problem-quite-confusing-t261767.html
    http://www.beatthegmat.com/mixture-ratio-problem-2-t191643.html

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