First find how many dogs get adopted each month by multiplying the number of dogs by their chance of getting adopted: 30 dogs * 50% = <<30*50*.01=15>>15 dogs
Then do the same thing for the cats: 28 cats * 25% = <<28*25*.01=7>>7 cats
And do the same thing for the lizards: 20 lizards * 20% = <<20*20*.01=4>>4 lizards
Now add up the number of each kind of pet to find the initial total number of pets: 30 dogs + 28 cats + 20 lizards = <<30+28+20=78>>78 pets
Now subtract all the pets that get adopted in one month from the initial number of pets: 78 pets - 15 dogs - 7 cats - 4 lizards = <<78-15-7-4=52>>52 pets
Now add the extra 13 pets the shelter takes in that month to find the final number of pets: 52 pets + 13 pets = <<52+13=65>>65 pets
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