His $20 bills amount to 4 x $20 = $<<4*20=80>>80.
So the total amount of the $10 and $20 bills is $80 + $50 = $<<80+50=130>>130.
Hence, the remaining $5 bills amount to $150 - $130 = $20.
This means that there are $20/$5 = <<20/5=4>>4 $5 bills.
There are also $50/$10 = 5 $10 bills.
Therefore, Samuel has 4 + 4 + 5 = <<4+4+5=13>>13 bills in his wallet.
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