<human>:  Trey is hanging wall decorations around his house. He uses a nail for each of two-thirds of them, a thumbtack for each of two-fifths of the rest, and a sticky strip for each of the other decorations. He used 15 sticky strips. How many nails did Trey use?
<bot>: How many thumbtacks and sticky strips did Trey use? ** 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
How many total decorations did Trey use? ** The 25 decorations were 1/3 of the total decorations, so he used 25 / 1/3 = 75 total decorations
How many nails did Trey use? ** The nails were 2/3 of the decorations, so Trey used 75 decorations * 2/3 = <<2/3*75=50>>50 nails
#### 50