Let $\mathbf { a } , \mathbf { b }$ and $\mathbf { c }$ be positive real numbers,
$$\begin{aligned} & a \cdot b + a \cdot c = 45 \\ & \frac { a } { b + c } = \frac { 4 } { 5 } \end{aligned}$$
Accordingly, what is the sum $\mathbf { a } + \mathbf { b } + \mathbf { c }$?
A) 9
B) 18
C) 27
D) $\frac { 9 } { 2 }$
E) $\frac { 27 } { 2 }$