# One older then the other

• May 31st 2007, 01:47 PM
Godfather
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?
• May 31st 2007, 01:53 PM
Jhevon
Quote:

Originally Posted by Godfather
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
• May 31st 2007, 03:27 PM
Soroban
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?

I use a chart for most age problems.

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: .$\displaystyle x \:=\:2(x - 6)$