Question

Helen is 8 years older than Jane. Twenty years ago Helen was three times as old as Jane. How old is each now?

Answer 1

Let the age of the Jane be $x$

So age of Helen =  $x$ + 8

Twenty years ago,

Age of Jane = $x$ - 20

And age of Helen = $x$ + 8 - 20 = $x$ - 12

Helen was three times as old as Jane

$x$ - 12 = 3 ($x$ - 20)

$x$ - 12 = 3 $x$ - 60

Add - 3$x$ on both sides,

$x$ - 3 $x$ - 12 = 3 $x$ - 3 $x$ - 60

-2$x$ - 12 = - 60

Add  12 on both sides

-2$x$ - 12  + 12 = - 60 + 12

-2$x$ = - 48

Divide both side by -2

$\frac{-2x}{-2}=\frac{-48}{-2}$

$x$ = 24

Age of Jane = 24 yrs

Age of Helen = 32 yrs

Answer 2

Helen is 16 and Jane is 8