\(\hept{\begin{cases}2a+3b+2c=5\\5a+4b+c=55\\a+b-4c=24\end{cases}}\Leftrightarrow8a+8b-c=5+55+24\)
\(\Leftrightarrow8a+8b-c=84\)
\(\Leftrightarrow8\left(a+b\right)-c=84\)
\(\Leftrightarrow8\left(a+b\right)=84+c\)
\(\Rightarrow a+b+c=84\)
\(\Rightarrow TBC\left(a,b,c\right)=\frac{84}{3}=28\)