Question 514024
You started on the right track, but you actually only need one variable.  Let x be the amount of money both Lily and Sara have at first.  We have a relationship in words between the amount of money Lily and Sara have now, and we need to convert this relationship into an algebraic equation.  First, Lily spent $18, so the amount of money Lily has now is x - 18.  Sara spent $25, so likewise the amount of money Sara has now is x - 25.  We know that Lily now has twice as much money as Sara, so we can write this fact algebraically as:

{{{ x - 18 = 2(x - 25) }}} (the amount of money Lily has now = two times the amount of money Sara has now)

Now we solve for x:

{{{ x - 18 = 2x - 50 }}} (distribute the 2 on the right hand side)
{{{ -18 = x - 50 }}} (subtract x from both sides)
{{{ 32 = x }}} (add 50 to both sides)

So we got x = 32.  Does this make sense?  If both Lily and Sara started with $32, Lily would now have $32 - $18 = $14, while Sara would now have $32 - $25 = $7, so Lily would now have twice as much money as Sara.  Thus $32 is the answer.