Jack is 6 years older than Jane. Six years ago he was twice as old as she was. How old is Jane now?

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- May 31st 2007, 01:47 PMGodfatherOne 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?

- May 31st 2007, 01:53 PMJhevon
- May 31st 2007, 03:27 PMSoroban
Hello, Godfather!

Quote:

Jack is six years older than Jane.

Six years ago he was twice as old as she was.

How old is Jane now?

Make a row for each person.

$\displaystyle \begin{array}{cccccc} & | & \quad & | & \quad & | \\ \hline

\text{Jack} & | & & | & &| \\ \hline

\text{Jane} & | & & | & & | \\ \hline

\end{array}$

Make a column for "Now".

$\displaystyle \begin{array}{cccccc} & | & \text{Now} & | & \quad & | \\ \hline

\text{Jack} & | & & | & &| \\ \hline

\text{Jane} & | & & | & & | \\ \hline

\end{array}$

Let $\displaystyle x$ = Jane's age now.

Then $\displaystyle x + 6$ = Jack's age now.

. . Write those in the "Now" column.

$\displaystyle \begin{array}{cccccc} & | & \text{Now} & | & \quad & | \\ \hline

\text{Jack} & | & x + 6 & | & &| \\ \hline

\text{Jane} & | &x & | & & | \\ \hline

\end{array}$

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

$\displaystyle \begin{array}{cccccc} & | & \text{Now} & | & \text{6 ago} & | \\ \hline

\text{Jack} & | & x + 6 & | & &| \\ \hline

\text{Jane} & | &x & | & & | \\ \hline

\end{array}$

Six year ago, both were six years younger.

. . Jack was only $\displaystyle x$ years old.

. . Jane was only $\displaystyle x - 6$ years old.

Write those in the second column.

$\displaystyle \begin{array}{cccccc} & | & \text{Now} & | & \text{6 ago} & | \\ \hline

\text{Jack} & | & x + 6 & | & x &| \\ \hline

\text{Jane} & | &x & | & x - 2 & | \\ \hline

\end{array}$

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

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