SOLUTION: 6 years ago Josie was 5 times as old as her Niece Dianne.How old is Dianne now if her age is one-third of her aunt'# Please help me.

Let Dianne's age is x years now.


Then Josie's age is 3x years, according to the condition.


Also, from the condition


    3x-6 = 5*(x-6).        ( <<<---===  6 years ago . . . )


All you need is to solve this equation.


    3x - 6 = 5x - 30

    30 - 6 = 5x - 3x

    24     = 2x

     x     = 24/2 = 12.


ANSWER.  Dianne is 12 years old.