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Thread: Mixture Sodium Chloride

  1. #1
    Super Member harpazo's Avatar
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    Mixture Sodium Chloride

    A tank contains 10,000 gallons of a solution that is 5% sodium chloride by volume. If 2,500 gallons of water evaporate from the tank, the remaining solution will be about what percent sodium chloride?

    My solution equation is as follows:

    0.95(x + 0.05) = 0.05(10,000 + 7500x

    This equation led to the wrong answer.
    Why is this equation wrong?
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  2. #2
    Member Walagaster's Avatar
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    Re: Mixture Sodium Chloride

    The tank contains 10000 x .05 = 500 gal. sodium chloride. After evaporation the tank contains 7500 gallons of which 500 is sodium chloride. So you have 500/7500 = .05 or 5% now.
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    Re: Mixture Sodium Chloride

    Quote Originally Posted by harpazo View Post
    A tank contains 10,000 gallons of a solution that is 5% sodium chloride by volume. If 2,500 gallons of water evaporate from the tank, the remaining solution will be about what percent sodium chloride?

    My solution equation is as follows:

    0.95(x + 0.05) = 0.05(10,000 + 7500x

    This equation led to the wrong answer.
    Why is this equation wrong?
    One reason your equation is wrong is x+ 0.05. What is x? Again define your variable. Is it in the same unit as 0.05?

    These sorts of questions usually don't require an equation to solve.

    You need to find two quantities and then express one as a percentage of the other.

    10 000 gallons of a solution :
    5% of 10 000 = 500 gallons is sodium chloride
    The other 9500 gallons is water.

    After evaporation:
    2500 gal of water evaporate: 9500 - 2500 =7000 gal of water left.

    There is still 500 gal of sodium chloride.

    There is a total of 7500 gal of solution.

    So, can you now work out

    "the remaining solution will be about what percent sodium chloride?"
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  4. #4
    Super Member harpazo's Avatar
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    Re: Mixture Sodium Chloride

    Quote Originally Posted by Walagaster View Post
    The tank contains 10000 x .05 = 500 gal. sodium chloride. After evaporation the tank contains 7500 gallons of which 500 is sodium chloride. So you have 500/7500 = .05 or 5% now.
    Are you saying that no equation is needed?
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  5. #5
    Super Member harpazo's Avatar
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    Re: Mixture Sodium Chloride

    Quote Originally Posted by Debsta View Post
    One reason your equation is wrong is x+ 0.05. What is x? Again define your variable. Is it in the same unit as 0.05?

    These sorts of questions usually don't require an equation to solve.

    You need to find two quantities and then express one as a percentage of the other.

    10 000 gallons of a solution :
    5% of 10 000 = 500 gallons is sodium chloride
    The other 9500 gallons is water.

    After evaporation:
    2500 gal of water evaporate: 9500 - 2500 =7000 gal of water left.

    There is still 500 gal of sodium chloride.

    There is a total of 7500 gal of solution.

    So, can you now work out

    "the remaining solution will be about what percent sodium chloride?"
    Is the needed equation 7500x = 500?
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    Re: Mixture Sodium Chloride

    Quote Originally Posted by harpazo View Post
    Are you saying that no equation is needed?
    I wouldn't bother with an equation. Just go step by step.
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    Re: Mixture Sodium Chloride

    Quote Originally Posted by harpazo View Post
    Is the needed equation 7500x = 500?
    You want to express 500 as a percentage of 7500.

    That is $\displaystyle \frac{500}{7500} * 100percent \approx6.67percent$.

    If you solve your equation you will get 0.0667 which is the same as 6.67%. So your equation is not wrong (given x is the fraction of the solution which is NaCl, not the percentage.)

    But, as I said before, an equation is not really necessary in this sort of problem. Just do it step by step, showing what each step is doing.
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  8. #8
    Super Member harpazo's Avatar
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    Re: Mixture Sodium Chloride

    Quote Originally Posted by Debsta View Post
    I wouldn't bother with an equation. Just go step by step.
    I totally get it. My goal, however, is to "master" the art of converting word problems to an equation leading to the right answer. This is the MAIN REASON why I joined the MHF.
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  9. #9
    Super Member harpazo's Avatar
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    Re: Mixture Sodium Chloride

    Quote Originally Posted by Debsta View Post
    You want to express 500 as a percentage of 7500.

    That is $\displaystyle \frac{500}{7500} * 100percent \approx6.67percent$.

    If you solve your equation you will get 0.0667 which is the same as 6.67%. So your equation is not wrong (given x is the fraction of the solution which is NaCl, not the percentage.)

    But, as I said before, an equation is not really necessary in this sort of problem. Just do it step by step, showing what each step is doing.
    What is NaCI?
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  10. #10
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    Re: Mixture Sodium Chloride

    Quote Originally Posted by harpazo View Post
    What is NaCI?
    Forgot your chemistry, eh? Na is the chemical abbreviation for sodium and Cl for chlorine. Sodium Chloride is common table salt. You could just type NaCl in google to find out.
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  11. #11
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    Re: Mixture Sodium Chloride

    Quote Originally Posted by harpazo View Post
    I totally get it. My goal, however, is to "master" the art of converting word problems to an equation leading to the right answer. This is the MAIN REASON why I joined the MHF.
    Yeah but sometimes that's not the best way to solve the problem. This problem is a good example of this.

    I don't think anyone on this forum would approach that problem by first finding an equation to solve.

    One of the skills in problem solving is to determine which sort of problems require an initial equation/s and which ones are best approached in the way I suggested above.

    In any case, if you want to form an equation, you MUST define what x is.
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  12. #12
    Super Member harpazo's Avatar
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    Re: Mixture Sodium Chloride

    Quote Originally Posted by Debsta View Post
    Yeah but sometimes that's not the best way to solve the problem. This problem is a good example of this.

    I don't think anyone on this forum would approach that problem by first finding an equation to solve.

    One of the skills in problem solving is to determine which sort of problems require an initial equation/s and which ones are best approached in the way I suggested above.

    In any case, if you want to form an equation, you MUST define what x is.
    Thank you. I do agree with you. An equation is not always needed but it's so much fun and mathematical.
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