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    Find two fractions...

    Find two fractions that are evenly spaced from 3/a and 7/2a.
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    Quote Originally Posted by ceasar_19134 View Post
    Find two fractions that are evenly spaced from 3/a and 7/2a.
    We are looking for two numbers, call them x and y such that:
    (3/a) + d = x
    x + d = y
    y + d = 7/(2a)
    where d is some constant.

    Putting all these together we get that
    3/a + 3d = 7/(2a)
    1/a + d = 7/(6a)
    d = 7/(6a) - 1/a = 7/(6a) - 6/(6a) = 1/(6a)

    So
    x = 3/a + d = 3/a + 1/(6a) = 18/(6a) + 1/(6a) = 19/(6a)

    y = x + d = 19/(6a) + 1/(6a) = 20/(6a) = 10/(3a)

    To check:
    7/(2a) =? y + d = 20/(6a) + 1/(6a) = 21/(6a) = 7/(2a) Check!

    So the two intermediate numbers are 19/(6a) and 10/(3a).

    -Dan
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