A man is x years old while his son is y years old, the sum of their ages is equal to twice the different of their ages, the product of their ages is 675, find the ages of the man and his son.

Let's try a creative solution not involving algebra directly. 
Factors of 675 are 
1, 675 
3, 225 
5, 135 
9, 75 
15, 45 <--- most likely! 
25, 27 



Now we verify... 
15+45= 2( 45-15) ? 
yes! 

so x=15, y=45