When I first got to Buenos Aires (March of 2007), the closest one to the place I was living Suipacha & Santa Fe) charged AR$20/milk crate. Then there was a blackout due to rain on exactly half of the block- up to and including, but not past this location- and for two days I didn't have clean laundry. But I did learn that one block over they charged AR$14 and guaranteed same day.
When I left my neighborhood near Facu de Medicina/Once 3 months ago (but roughly 3 1/2 years after first arriving), the place I was going to charged AR$10/ milk crate because my previous place had gone up to AR$12 or AR$13.
Your neighborhood will definitely determine your laundry cost. The $15 when the quote was AR$10 sounds like a runaround. And AR$15 because they're bed sheets also sounds like a scam. But if they are the only option, they are the only option. But I doubt it would take long to find another 2 or 3 options 1 block further.