How old are they both now?

Question

Ten years ago a man was as old as his wife is now. The man is now twice as old as his wife was then. How old are they both now?

 

Answer 1

M:  age of man today

W:  age of wife today.  

 

We set up these 2 equations from the problem:  

 

M - 10 = W          [ten years ago the man was as old as the wife is today]

2*(W - 10) = M       [the man is twice as old as the wife was ten years ago]

 

Plugging the equation for W into the second equation and solving yields:

 

2*[(M - 10) - 10] = M

2*[M - 20] = M

2*M - 40 = M

M = 40. 

 

Since W = M - 10, then W=30.