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Thread: Number Line With r, s, and t

  1. #1
    Senior Member harpazo's Avatar
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    Number Line With r, s, and t

    On the number line, if r < s, if p is halfway between r and s, and if t is halfway between p and r, then (s - t)/(t - r) =

    A. 1/4
    B. 1/3
    C. 4/3
    D. 3
    E. 4

    The book tells me that the distance from r to t is x, the distance from t to p is x and the distance from p to s is 2x.

    The book concludes that
    (s - t)/(t - r) = (x + 2x)/x, which of course is 3.

    I do not understand the logic here.
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Number Line With r, s, and t

    I would let:

    $\displaystyle s-r=4d$

    Then:

    $\displaystyle p-r=2d$

    And:

    $\displaystyle t-r=d$

    Subtracting the third equation from the first, we obtain:

    $\displaystyle s-t=3d$

    Hence:

    $\displaystyle \frac{s-t}{t-r}=\frac{3d}{d}=3$
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  3. #3
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    Re: Number Line With r, s, and t

    Quote Originally Posted by harpazo View Post
    On the number line, if r < s, if p is halfway between r and s, and if t is halfway between p and r, then (s - t)/(t - r) =

    A. 1/4
    B. 1/3
    C. 4/3
    D. 3
    E. 4

    The book tells me that the distance from r to t is x, the distance from t to p is x and the distance from p to s is 2x.

    The book concludes that
    (s - t)/(t - r) = (x + 2x)/x, which of course is 3.

    I do not understand the logic here.
    Look at at a simple number line.Number Line With r, s, and t-numline.png
    Thanks from topsquark
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  4. #4
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    Re: Number Line With r, s, and t

    Quote Originally Posted by Plato View Post
    Look at at a simple number line.Click image for larger version. 

Name:	numline.png 
Views:	1 
Size:	1.7 KB 
ID:	39147
    Yes that's exactly what I would do, except I would leave off the numbers and just mark equal lengths. Always draw a diagram if you can.
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  5. #5
    Senior Member harpazo's Avatar
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    Re: Number Line With r, s, and t

    Thank you everyone.
    Thanks from MarkFL
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