Question 711598
ANSWER::
Let Lucy's age be X and Amy's age must now be 2X (Due to the fact that it is said Amy is twice as old as Lucy) 
The current age of Amy is 2X and for Lucy is X
Then, Three yrs to come we have (2x+3->Age for Amy and X+3->age for Lucy)
Also the sum of their age will be 42:-> (2X+3)+ (X+3)=42
open the brackets to have 3X+6=42, solve for X now as You will get X= 12 
THEREFORE, Amy's age is 2X= 2*12= 24 years