The problem is that you aren't dealing with an inverted strangle. You have sold two puts, one synthetic and one naked. Let's take a deep dive into equivalent positions.
There are 6 basic synthetic positions relating to combinations of put options, call options and their underlying stock (the Synthetic Triangle):
Synthetic Long Stock = Long Call + Short Put
Synthetic Short Stock = Short Call + Long Put
Synthetic Long Call = Long Stock + Long Put
Synthetic Short Call = Short Stock + Short Put
Synthetic Short Put = Long Stock + Short Call
Synthetic Long Put = Short Stock + Long Call
These are all variations of S + P - C = 0 which is the core of put/call parity.
Note that # 5 which shows that a short put equals a covered call (+ STK - Call). As applied to your example, you bought the stock and sold a $45 call. This is equivalent to having sold a $45 put. Then, you sold a $55 put, ending up with one short $45 put and one short $55 put. This isn't an Inverted Short Strangle (often called a Guts Strangle). It's two naked/short puts. See the reply from D Stanley explaining the P&L of the position.
If you were executing the position all at once, it would be better to sell the equivalent OTM strangle because B/A spreads on OTM options tend to be much narrower and you'll avoid the possibility of early assignment (assuming these are American options).
Your two equations are:
+STK + $45p = + $45c
+STK + $55p = + $55c
Factoring both equations you end up with:
+STK + $45p = + $45c
+STK - $55c = - $55p
or
-STK - $45p = - $45c
+STK - $55c = - $55p
Selling the $45c and the $55p would be an Inverted Strangle. Add both sides:
-$45c - $55p = - STK - $45p + STK - $55c
Simplify:
-$45c - $55p = - $45p - $55c
(ITM $45c/55p strangle = OTM $45p/55c strangle)
Clear as mud?