The ratio of red marbles to black marbles is 9:4, this implies:
[tex]\frac{x+80}{x}=\frac{9}{4}[/tex]By cross-multiplying and solving for x, we have:
[tex]\begin{gathered} 9x=4(x+80) \\ 9x=4x+320 \\ 9x-4x=320 \\ 5x=320 \\ x=\frac{320}{5} \\ x=64 \end{gathered}[/tex]Thus, the number of red marbles is 64+80=144 and the number of black marbles is 64.
Hence, the total number of marbles in the bag is:
[tex]144+64=208\text{ marbles}[/tex]