I would consider reading up on Borax a little more before using it, especially since I was told to lay out Borax when we had some ants coming in our back door at my last house.
If what we have is Mold then mix:
2 parts water
1 part Hydrogen Peroxide (check out its many benefits)
The greatest part about these things is that they are super simple, and I don't even have to spend a cent! I might have to buy a good brush to get into that depression between the tiles however...... I wonder if there are any bamboo brushes out there?