To find the marked down price, we begin with the original price, x.
Then we multiply the original price by 55% and get 0.55x.
Then we subtract that from the original price x, and get the reduced price, 
x-0.55x.

So the reduced price is $89.55, we make them equal:

x-0.55x = 89.55

We write x as 1.00x

1.00x-0.55x = 89.55

      0.45x = 89.95

          x = 89.95/0.45

          x = 199.888888888888888888888888888888888888888888888889

You can round that up to $199.89.

Edwin