David is twice as old as Mark. Nine years ago, David was three times as old as Mark was then. How old is David in years?

Question

David is twice as old as Mark. Nine years ago, David was three times as old as Mark was then. How old is David in years? Thanks!

Answer 1

Let d = David's current age

Let m = Mark's current age

 

David is twice as old as Mark:

d= 2m     {equation 1}

 

9 years ago David was 3 times as old as Mark was then:

d-9 = 3(m-9)    {equation 2}

 

Replace d with 2m in equation 2 and solve for m

 

2m - 9 = 3(m-9)

2m - 9 = 3m - 27

27 - 9 = 3m - 2m

18 = m

 

Mark is 18

David is 2(18) =36

Answer 2

Set X = the age of Mark 9 years ago, so 3X was the age of David 9 years ago.

 

Now, Mark is X+9 years old, and David is 2*(X+9) = 2X+18 years old.

 

Note that David was 3X years old 9 years ago, and now he is also 3X+9 years old,

 

So:   3X+9 = 2X+18,  solve for X you get, X=9.

 

So David is 3*9+9 = 36 years old now.