If $$\frac{{a + b}}{c} = \frac{6}{5}$$   and $$\frac{{b + c}}{a} = \frac{9}{2},$$   then what is the value of $$\frac{{a + c}}{b}?$$

$$\eqalign{ & \frac{{\left( {a + b} \right)}}{c} = \frac{6}{5} \cr & \frac{{\left( {b + c} \right)}}{a} = \frac{9}{2} \cr & \frac{{\left( {a + c} \right)}}{b} = ? \cr & c = 5,\,\frac{{\left( {b + c} \right)}}{a} = \frac{9}{2} \cr & \Rightarrow \frac{{b + 5}}{2} = \frac{9}{2} \cr & b = 4,\,a = 2 \cr & \Rightarrow \frac{{\left( {a + c} \right)}}{b} = \frac{{2 + 5}}{4} \cr & \Rightarrow \frac{{\left( {a + c} \right)}}{b} = \frac{7}{4} \cr} $$