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Ratios and Proportions

  1. Sep 16, 2010 #1
    1. The problem statement, all variables and given/known data

    Let s-a : s-b : s-c :: 1:2:3

    then how do we find a:b:c from this?


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 16, 2010 #2

    Borek

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    Staff: Mentor

    Try to format your expression in such a way that it is unambiguous what you are looking for.
     
  4. Sep 16, 2010 #3
    How do I do that?
     
  5. Sep 16, 2010 #4

    Borek

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    Staff: Mentor

  6. Sep 16, 2010 #5

    Mark44

    Staff: Mentor

    Rewrite this proportion as three equations. The proportion is saying is that s - b is 2 times s - a, s - c is 3 times s - a, and s - c is (3/2) times s - b.

    That should give you somewhere to start.
     
  7. Sep 16, 2010 #6
    Thanks alot :smile:
     
  8. Sep 16, 2010 #7

    HallsofIvy

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    Staff Emeritus
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    That's slightly confusing because it represents several proportions together.
    You can analyze it as [itex]s-a: s-b::1:2[/itex], [itex]s-b: s-c::2: 3[/itex], and [itex]s-a: s-c::1: 3[itex]. Those can be written as fraction:
    [tex]\frac{s-a}{s-b}= \frac{1}{2}[/tex]
    [tex]\frac{s-b}{s-c}= \frac{2}{3}[/tex]
    and
    [tex]\frac{s-a}{s-c}= \frac{1}{3}

    The first equation can be rewritten as 2(s- a)= s- b, 3(s-b)= 2(s- c), and 3(s-a)= s- c.

    You can solve each of those for s: 2s- 2a= x- b so s= 2a- b. 3s- 3b= 2s- 2c so s= 3b- 2c. 3s- 3a= s- c so 2s= 3a- c or s= (3/2)a- (1/2)c.

    Now put them back together: s= 2a- b= (2/3)a- (1/2 c, s= 2a- b= 3b- 2c. You should be able to find the relationships between a, b, and c from that.
     
  9. Sep 16, 2010 #8
    That made it more clear.
    I got a:b:c :: 5:4:3
    Thanks alot Hallsofivy
     
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