The number of adopted puppies in the second week is 2/5*20 puppies = <<2/5*20=8>>8 puppies
In the third week, Yuri adopted 2 * 8 puppies = <<2*8=16>>16 puppies
In the fourth week Yuri adopted ten more puppies than the third week, which totals 10 puppies + 20 puppies = <<10+20=30>>30 puppies.
The total number of puppies in the four weeks is 30 puppies +16 puppies + 8 puppies + 20 puppies = <<30+16+8+20=74>>74 puppies
#### 74