Answer :
Solution:
Let the number of republicans be
[tex]r[/tex]Let the number of democrats be
[tex]d[/tex]For a recent Congress, there were 10 more Democrats than Republicans in the U.S. Senate.
This can be represented below as
[tex]d=r+10[/tex]The ratio of democrats to republicans is
[tex]\frac{d}{r}=\frac{11}{9}[/tex]put d=r+10
[tex]\begin{gathered} \frac{d}{r}=\frac{11}{9} \\ \frac{r+10}{r}=\frac{11}{9} \\ cross\text{ multiply} \\ 11r=9(r+10) \\ 11r=9r+90 \\ 11r-9r=90 \\ 2r=90 \\ \frac{2r}{2}=\frac{90}{2} \\ r=45 \end{gathered}[/tex]Substitute r =45 in the equation belo
[tex]\begin{gathered} d=r+10 \\ d=45+10 \\ d=55 \end{gathered}[/tex]Hence,
The final answer is
55 democrats
45 republicans