my try

1. {c}+[a]+{b} = 4.0 ==> {c}+{b} is integer
2. (1)+(2)
[b]+[c]+{c}+{b}+2{a} = 8.2
==> 2{a}=0.2 or 1.2
==> {a}=0.1 or 0.6

{a}=0.1
==> {c}=0.8 and [b]=2
==> {b}=0.2 and [c]=5
==> [a]=3
==> (3.1, 2.2, 5.8)

{a}=0.6
==> {c}=0.3 and [b]=2
==> {b}=0.7 and [c]=4
==> [a]=3
==> (3.6, 2.7, 4.3)