Complicated symbols make this problem easy

Algebra Level 3

Given the systemb+a+{c}=16\lfloor b\rfloor+ \lceil a\rceil+ \{c\}=16 c+b+{a}=11.3\lfloor c\rfloor+ \lceil b\rceil +\{a\}=11.3 a+c+{b}=9.7,\lfloor a\rfloor+ \lceil c\rceil +\{b\}=9.7 , what is a+b+ca+b+c?

Note:
x\lfloor x\rfloor Represents the floor function, which takes the greatest integer smaller or equal to x.
x\lceil x\rceil represents the ceiling function, which takes the smallest integer greater or equal to x.
Finally, {x}\{x\} represents the fractional part function.

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