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Math Help - Ratio Proportion

  1. #1
    Junior Member MoniMini's Avatar
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    Post Ratio Proportion

    I'm stuck up with this too

    The ages of Katheline and Gwen are in the ratio 2 : 3. After 12 years, their ages will be in the ratio 11 : 15. The age of Gwen is-
    a) 32 years
    b) 42 years
    c) 48 years
    d) 56 years

    Any help will be appreciated.

    Thanks a Lot!
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  2. #2
    Super Member
    earboth's Avatar
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    Re: Ratio Proportion

    Quote Originally Posted by MoniMini View Post
    I'm stuck up with this too



    Any help will be appreciated.

    Thanks a Lot!
    Let x denote the age of Katheline and y the age of Gwen.

    Then you know:

    \frac xy = \frac23

    \frac{x+12}{y+12} = \frac{11}{15}

    This is a system of simultaneous equations which you can solve easily.
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  3. #3
    Junior Member MoniMini's Avatar
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    Re: Ratio Proportion

    Ok.......
    Initially I had come to this conclusion but
    I'm having some troubles after this equation.
    How to find the values of x and y?
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  4. #4
    Junior Member mathbyte's Avatar
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    Post Re: Ratio Proportion

    Usually in solving a system of simultaneous equations, you wind up manipulating one of them so you can express on variable in terms of the other. That allows you to substitute that variable into the other equation.

    Let's take this instance as an example: let's call the top equation Equation 1, and the lower one Equation 2.

    Equation 1 can be re-worked so we can express x in terms of y:

    x/y = 2/3

    3x = 2y

    So we can then figure out

    x = 2y/3

    Knowing that, we can then substitute this value for x into Equation 2. When you do that, what do you get then?
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  5. #5
    Junior Member MoniMini's Avatar
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    Cool Re: Ratio Proportion [SOLVED]

    Oooh! I got it now!
    \frac xy = \frac23
    and
    \frac{x+12}{y+12} = \frac{11}{15}

    then

    \15 (x + 12) =  11 (y + 12)

    = 15x + 180 = 11y + 132

    = 180 - 132 = 11y - 15x

    = 48 = 11y - 15x

    and if

    \frac xy = \frac23

    then

    x = \frac {2y} 3

    then

    15x = \frac {15} 1 \!\cdot\! \frac {2y} 3
    = \frac {30y}3

    then we go back to

    = 48 = 11y - 15x

    so that becomes

    48 = 11y - \frac {30y}3
    = 48 = 11y - 10y
    = 48 = y

    So, if x is Katheline and y is Gwen, then
    Gwen is 48 years old.

    Whoa!!
    Thnx a lot @earboth and @mathbyte!

    ~MoniMini
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