Algebra Word Problem

Question

Six years ago, Ed was three years less than twice as old as Jim.  In eight years Ed will be one year less than three times as old as Jim was six years ago.  How old are they now?

Answer 1

Hi, Peter.

Let X = Jim's age now

Let Y = Ed's age now

 

Y - 6 = 2(X - 6) - 3

Y + 8  = 3(X - 6) - 1

So:

Y - 6 = 2(X - 6) - 3

Y = 2X - 12 - 3 + 6 = 2X - 9

Now substitute into 2nd equation:

 

Y + 8 = 3(X - 6) - 1

(2X - 9) + 8 = 3(X - 6) - 1

2X - 1 = 3X - 18 - 1

X = 18

 

So, X = 18 (Jim's age)

 

Ed = 2X - 9 = 27

 

Jim is 18 years old

Ed is 27 years old