Cristian eats 3/4*80 = <<3/4*80=60>>60 white cookies from the jar, 3/4 of the total number of white cookies in the cookie jar.
The number of white cookies remaining in the cookie jar is 80-60 =<<80-60=20>>20
In his cookie jar, Cristian also has 80+50 = <<80+50=130>>130 black cookies.
He eats 1/2*130 = <<130*1/2=65>>65 black cookies from the cookie jar.
He remains with 130-65 = <<130-65=65>>65 black cookies after eating half of them.
In total, Cristian has 65+20 = <<65+20=85>>85 cookies remaining in the jar.
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