Answer:
not possible.
Step-by-step explanation:
number of invitations luanne  has to address after x days = 120-15x
number of invitations  Darius has to address after x days =  120 + 15(7-x)
so, if the number of invitations should be the same for both of them, 
we have to equate their number of invitations
120-15x =  120 + 15(7-x)
subtracting 120 from both the sides, 
-15x = 15(7-x) = 105 -15x
adding we 15x on both sides, we wont find any solution for x.
so, this isnt possible or the question must be wrong.