The fastest approach here might be to plug in the answer choices.James is twice as old as Stephanie, who, 4 years ago, was 3 times as old as Kate. If, 5 years from now, the sum of their (all 3 people) ages will be 51, how old is Stephanie?
A) 6
B) 10
C) 14
D) 20
E) 24
Having said that, here's one possible algebraic approach.
Let x = Stephanie's present age.
James is twice as old as Stephanie
So 2x = James' present age.
4 years ago, Stephanie's was 3 times as old as Kate
In other words, 4 years ago, Kate's age was 1/3 of Stephanie's age.
4 years ago, Stephanie'sage was x-4, so Kate's age 4 years ago, was (x-4)/3
So, Kate's present age = (x-4)/3 + 4
In 5 years . . .
Stephanie's age = x + 5
James' age = 2x + 5
Kate's age = (x-4)/3 + 4 + 5
5 years from now, the sum of their ages will be 51
So (x + 5) + (2x + 5) + (x-4)/3 + 4 + 5 = 51
Simplify: 3x + (x-4)/3 + 19 = 51
Subtract 19 from both sides: 3x + (x-4)/3 = 32
Multiply both sides by 3: 9x + (x-4) = 96
Solve . . . [spoiler]x = 10[/spoiler]
Answer: B
If anyone is interested, we have a free video on solving word problems involving past and future ages: https://www.gmatprepnow.com/module/gmat- ... ems?id=908
Cheers,
Brent
