SOLUTION: Hi alan and bob share a sum of money. If alan gives1/4 of his share to bob, bob will have twice as much as alan. What was the ratio of alans share to bobs share at first. thank

Let A = amount of Alan's money (shares ?)
    B = amount of Bob's  money.


The condition says that  = 2.    (1)


Simplify the ratio in the left side, step by step. You will have

 =  =  +  =  +  =  +  =  + .


So we can write (1) in an equivalent form

 +  = 2,


which implies  

 =  - ,  ====>   =   ====>   =  = .


Answer.  The ratio of Alan' share to Bob' share at first was   = .