Trey used 15 sticky strips for 3/5 of the remaining decorations after using nails, so he used 15 * / 3/5 = 25 thumbtacks and sticky strips
The 25 decorations were 1/3 of the total decorations, so he used 25 / 1/3 = 75 total decorations
The nails were 2/3 of the decorations, so Trey used 75 decorations * 2/3 = <<2/3*75=50>>50 nails
#### 50