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Math Help - Word Problem And Equation

  1. #1
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    Word Problem And Equation

    I have two problems right now the 1st is an equation

    1, Two people walk 240 meters at a constant speed
    Person A takes 100 more steps than the other,
    Person B's steps are 20cm longer, Find how mant steps they take

    2. I did most of the problem but I can't get any farther on this
    9(u^2+uv+v^2)=7(u+v)^2
    u=2^(x+y)
    v=3^(x-y)

    The orignal problem is
    Solve System
    4^(x+y)=27+9^(x-y)
    8^(x+y)-21*2^(x+y)=27^(x-y)+7*3^(x-y-1)
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  2. #2
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    Quote Originally Posted by AHDDM View Post
    I have two problems right now the 1st is an equation

    1, Two people walk 240 meters at a constant speed
    Person A takes 100 more steps than the other,
    Person B's steps are 20cm longer, Find how mant steps they take

    ...
    Hello,

    let the number of steps of A be: x
    let the number of steps of B be: x - 100

    let the length of one step of A be: y
    let the length of one step of B be: y + 0.2

    Then you have:

    A:\ x \cdot y = 240~\implies~\boxed{y=\frac{240}{x}}

    B:\ (x-100)(y+0.2)=240 . Substitute y by the term of the equation A:

    (x-100)\left(\frac{240}{x}+0.2\right)=240

    I'll leave the rest for you.
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by AHDDM View Post
    2. I did most of the problem but I can't get any farther on this
    9(u^2+uv+v^2)=7(u+v)^2
    u=2^(x+y)
    v=3^(x-y)

    The orignal problem is
    Solve System
    4^(x+y)=27+9^(x-y)
    8^(x+y)-21*2^(x+y)=27^(x-y)+7*3^(x-y-1)
    It looks like your approach is right, though I'm not sure where you got that u, v equation from.

    4^{x+y}=27+9^{x-y}
    and
    8^{x+y}-21*2^{x+y}=27^{x-y}+7*3^{x-y-1}

    Let's rewite these:
    2^{2(x+y)} = 27 + 3^{2(x-y)}
    and
    2^{3(x+y)} - 21*2^{x+y} = 3^{3(x-y)} + \frac{7}{3}*3^{x-y}

    Let u = 2^{x + y} and v = 3^{x - y}.

    Then we have
    u^2 = 27 + v^2
    and
    u^3 - 21u = v^3 + \frac{7}{3} \cdot v

    As the graph below shows (use x = u and y = v) you are done. The graphs do not intersect, so there are no solutions.

    -Dan
    Attached Thumbnails Attached Thumbnails Word Problem And Equation-system.jpg  
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  4. #4
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    for the word problem I am getting to x^2-100x-12000=0 and from there no logical solutions coming out and it doesn't come out cleanly from quadratic formula
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  5. #5
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by AHDDM View Post
    for the word problem I am getting to x^2-100x-12000=0 and from there no logical solutions coming out and it doesn't come out cleanly from quadratic formula
    Check your work. The quadratic I'm getting is
    x^2 - 10x - 12000 = 0

    -Dan
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