math

Assume x and y have 5:3 profit sharing ratio respectivly and a new member enters by taking 1/5 from x and 1/3 from y.what will be the new ratio of the three people?

asked by ruth
  1. The original proportion: x : y = 5:3 ---> x/y = 5/3 ---> x = 5y/3
    after change:
    first member : (4/5)x or 4x/5
    2nd member: (2/3)y or 2y/3
    new member: (1/5)x + (1/3)y or x/5 + y/3
    new ratio : 4x/5 : 2y/3 : (x/5 + y/3)
    = 4(5y/3)/5 : 2y/3 : (5y/3)/5 + y/3)
    = 4y/3 : 2y/3 : 2y/3
    = 4 : 2 : 2
    = 2 : 1 : 1

    check: suppose the original investments were $600 and $360
    (notice 600:360 = 5:3)
    first member left with 480
    2nd member left with 240
    new member has 120+120 = 240
    ratio = 480 : 240 : 240 = 2:1:1
    my answer is plausible

    posted by Reiny
  2. how do we get the 4x/5 and 2y/3

    posted by ruth
  3. First member started with x
    you took 1/5 away, leaving him with 4/5
    (4/5)x = 4x/5

    same steps for 2y/3

    posted by Reiny

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