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Math Help - Word Problem equality

  1. #1
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    Word Problem equality

    The concentration of toxic chemical in a spring fed lake is given by the equation c(x)= 50x/x^2+3x+6, where c is given in grams per litre and x is the time in days. Determine when the concentration of the chemical is 6.16 g/L.

    50/x^2+3x+6= 6.16

    50/x^2+3x+6 (x^2+3x+6) (6.16) = 6.16(6.16) (x^2+3x+6)

    50(6.16)= 1(x^2+3x+6)

    308=x^2+3x+6

    0=x^2+3x+6-308
    0=x^2+3x-302


    Then solve using quadratic formula???? Im not sure if this is right.
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  2. #2
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    Quote Originally Posted by Skoz View Post
    The concentration of toxic chemical in a spring fed lake is given by the equation c(x)= 50x/x^2+3x+6, where c is given in grams per litre and x is the time in days. Determine when the concentration of the chemical is 6.16 g/L.

    50/x^2+3x+6= 6.16
    Are we to assume that this is 50/(x^2+ 3x+ 6)= 6.16 and not (5/x^2)+ 3x+ 6= 6.16? Please use parentheses!

    [/quote]50/x^2+3x+6 (x^2+3x+6) (6.16) = 6.16(6.16) (x^2+3x+6)[/quote]
    Okay, you are multiplying both sides by x^2+ 3x+ 6 to get rid of the fraction but why are you multiplying both sides by 6.16?

    50(6.16)= 1(x^2+3x+6)
    No, (6.16)(6.16) is NOT 1! I suppose you meant to divide both sides by 6.16

    308=x^2+3x+6

    0=x^2+3x+6-308
    0=x^2+3x-302


    Then solve using quadratic formula???? Im not sure if this is right.
    And since 50(6.16)= x^2+ 3x+ 6 is not correct, the rest is wrong.

    If you divide both sides by 6.16 you get x^2+ 3x+ 6= 50/6.16= 8.117, approximately so your equation is x^2+ 3x+ 6- 8.117= x^2+ 3x- -2.117= 0 and you can use the quadratic equation to solve that.
    Just multiply both sides of 50/(x^2+ 3x+ 6)= 6.16 by x^2+ 3x+ 6 to get
    x^2+ 3x+ 6=
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  3. #3
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    I have this exact same question but mine states

    (50x)/(x^2+3x+6)= 6.16

    How would I solve this?
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  4. #4
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    Quote Originally Posted by willman32 View Post
    I have this exact same question but mine states

    (50x)/(x^2+3x+6)= 6.16

    How would I solve this?
    let k = 6.16

    \frac{50x}{x^2+3x+6} = k

    50x = kx^2 + 3kx + 6k

    0 = kx^2 + (3k-50)x + 6k

    x = \frac{(50-3k) \pm \sqrt{(3k-50)^2 - 24k^2}}{2k}

    get out your calculator ...


    I find two valid solutions.
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  5. #5
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    is there a general way to solve these types of problems?
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  6. #6
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    Quote Originally Posted by willman32 View Post
    is there a general way to solve these types of problems?
    the way I showed you is general ... do you mean "easy" ?
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