Results 1 to 3 of 3

Math Help - One older then the other

  1. #1
    Junior Member Godfather's Avatar
    Joined
    Feb 2007
    Posts
    34

    One older then the other

    Jack is 6 years older than Jane. Six years ago he was twice as old as she was. How old is Jane now?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by Godfather View Post
    Jack is 6 years older than Jane. Six years ago he was twice as old as she was. How old is Jane now?
    Let Jane's age now be x
    Then Jack's age is x + 6

    Six years ago, Jack's age was x and this was twice Jane's age six years ago (which is x - 6). So we have:

    x = 2(x - 6)
    => x = 2x - 12
    => x = 12 --------> Jane's age now
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,915
    Thanks
    779
    Hello, Godfather!

    Jack is six years older than Jane.
    Six years ago he was twice as old as she was.
    How old is Jane now?
    I use a chart for most age problems.


    Make a row for each person.
    \begin{array}{cccccc} & | & \quad & | & \quad  & | \\ \hline<br />
\text{Jack} & | & & | & &| \\ \hline<br />
\text{Jane} & | & & | & & | \\ \hline<br />
\end{array}


    Make a column for "Now".
    \begin{array}{cccccc} & | & \text{Now} & | & \quad & | \\ \hline<br />
\text{Jack} & | & & | & &| \\ \hline<br />
\text{Jane} & | & & | & & | \\ \hline<br />
\end{array}


    Let x = Jane's age now.
    Then x + 6 = Jack's age now.
    . . Write those in the "Now" column.

    \begin{array}{cccccc} & | & \text{Now} & | & \quad & | \\ \hline<br />
\text{Jack} & | & x + 6 & | & &| \\ \hline<br />
\text{Jane} & | &x & | & & | \\ \hline<br />
\end{array}


    Make a column for the other time period: "6 years ago".

    \begin{array}{cccccc} & | & \text{Now} & | & \text{6 ago} & | \\ \hline<br />
\text{Jack} & | & x + 6 & | & &| \\ \hline<br />
\text{Jane} & | &x & | & & | \\ \hline<br />
\end{array}


    Six year ago, both were six years younger.
    . . Jack was only x years old.
    . . Jane was only x - 6 years old.
    Write those in the second column.

    \begin{array}{cccccc} & | & \text{Now} & | & \text{6 ago} & | \\ \hline<br />
\text{Jack} & | & x + 6 & | & x &| \\ \hline<br />
\text{Jane} & | &x & | & x - 2 & | \\ \hline<br />
\end{array}


    It says, "Six years ago, Jack (x) was twice Jane's age (x-6)."

    . . and there is our equation: . x \:=\:2(x - 6)

    Follow Math Help Forum on Facebook and Google+

Search Tags


/mathhelpforum @mathhelpforum