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Math Help - Word problem

  1. #1
    Junior Member
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    Jul 2007
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    Word problem

    Hello all,

    Experiencing a brain freeze here. There are two related word problems in the book I am reading. The first one I solved, the second one is giving me fits. The first problem reads:

    How much water must be evaporated from 500 grams of a 10% salt solution in order to obtain a solution containing 15% salt?

    My solution was to make x represent the amount of water to be evaporated. My equation was:

    90% (500) - x = 85% (500 - x)

    Solving: 450 - x = 425 - .85x
    25 = .15x
    x = 166 2/3 grams

    which is correct.

    The second question states:

    Generalize Exercise 57 as follows: Let a, b, and d be positive real numbers with a < b < 100. Given a solution of d grams of salt water that is a% salt, how much water must be evaporated in order that the resulting mixture will be b% salt? Express the answer in terms of a, b, and d.

    Here I've tried expressing the equation as

    ad - x = b(d-x)

    Solving:
    ad - x = bd -bx
    ad - bd = x - bx
    d(a - b) = x (1 - b)
    (d(a - b))/(1 - b) = x

    However, this gives an incorrect answer with the original numbers. The solution given in the book is

    x = (d(b - a))/b

    I can't for the life of me figure out how they got to this equation. Please help!
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Hello, earachefl!

    Your original solution is correct.
    In the generalization, your set-up is wrong . . .


    How much water must be evaporated from 500 grams of a 10% salt solution
    in order to obtain a solution containing 15% salt?

    My solution was to make x represent the amount of water to be evaporated.

    My equation was: . 90\%(500) - x \;= \;85\%(500 - x) . Right!
    Look at what we've got . . .

    \text{We have: }\;\underbrace{90\%}_{1 - 10\%}(500) - x \;=\;\underbrace{85\%}_{1 - 15\%}(500 - x)


    We have d grams of solution which is a\% salt.
    We evaporate x grams of water to get a solution which is b\% salt.

    The general equation is: . (1 - a)d - x \;=\;(1 - b)(d - x)

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  3. #3
    Junior Member
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    D'oh!!

    thank you!
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