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

# Answer

50
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
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?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
50
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?
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