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Math Help - Ratio and Model

  1. #1
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    Ratio and Model

    Would appreciate if anyone can help on the following question:

    When F was 66 years old, the ratio of A's age to R's age was 3:1 when R was 5 yrs old, the ratio of F's age to A's age was 3:1 find the ratio of F's age to R's age when A is 30 yrs old?
    Last edited by Michelletham; October 5th 2011 at 07:23 AM. Reason: Uppercase error
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  2. #2
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    Re: Ratio and Model

    F= 66

    A:R = 24:8



    ----------------

    R = 5

    F:A = 63:21


    -----------------

    A = 30

    72: 14





    Ill explain how I did this later, I have to run. Got to leave for my kiddos game.
    Last edited by Jman115; October 5th 2011 at 09:20 AM.
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  3. #3
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    Re: Ratio and Model

    So here is what I did:

    I made a list assuming the 3:1 ratios did not include decimals. So I started with the first one which was A:R. You can see my chart below. Keep in mind, based on the information the problem gave you, you should have been able to easily deduce that F was the oldest and R was the youngest.

    Ratio and Model-screen-shot-2011-10-06-8.09.01-am.png

    ON THE LEFT IN BROWN
    I started with multiples of 3 for A that well below 66 and seemed reasonable potential ages and worked my way down. The age I input for R was simply 1/3 the age of A because there is supposed to be a 3:1 ratio between their ages at this time.

    IN THE MIDDLE IN RED
    The first column represents the years in time it has been compared to the first column if R is now only 5. So if you look at the first row R was 14 in the brown, so in the red he is now 5 so it has been -9 years. In other words, everyone is 9 years younger. So if R lost 9 years, that means F and A are also 9 year young so I made those calculations in the F = and A = columns.

    In the first row of brown F was 66 and A was 42 so I simply subtracted 9 to get the values of 57 for F and 33 for A. When I finished that for every row I simply looked to see which pair of F and A ages had a 3:1 ratio F:A in the red columns. Once I found that I used that information for the green and final column.

    ON THE RIGHT IN GREEN:


    Since A is now 30 everyone is 9 years older than they were in the red column. You will notice the F = and A = in the red column that have a 3:1 ratio are bolded in black.

    So we know when
    R was 5
    A was 21
    and F was 66

    So now that A is 30 it is 9 years later.

    At this point I simply added 9 to F's and R's ages for a 72:14 ratio which can be reduced to -----> 36:7 ratio

    Click image for larger version. 

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  4. #4
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    Red face Re: Ratio and Model

    Quote Originally Posted by Michelletham View Post
    Would appreciate if anyone can help on the following question:

    When F was 66 years old, the ratio of A's age to R's age was 3:1 when R was 5 yrs old, the ratio of F's age to A's age was 3:1 find the ratio of F's age to R's age when A is 30 yrs old?
    Thank you very much! You are brilliant!
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  5. #5
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    Re: Ratio and Model

    let F,A,R be the ages of F,A,R today, so F=66 and A/R=3
    x years ago, R was 5, so R = 5 + x
    y years ago, A was 30, so A = 30 + y
    x years ago, we are told that the age of F then / the age of A then was 3:1,
    so (F-x) / (A-x) = 3.
    solving the equations
    (30+y) / (5+x) = 3 (first line)
    and
    (F-x)/(A-x) = 3
    leads to
    x=3 and y=-6 (i.e., the point when A is 30 is in the future).
    Now, we would like to compute the age of F y years ago over the age of R y years ago, which would then be
    (F-y)/(R-y) = (66- (-6))/(5+x-y) = 72 / 14 = 36 / 7.
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