Question

For a recent Congress, there were 10 more Democrats than Republicans in the U.S. Senate. This resulted in a ratio of11 Democrats to 9 Republicans. How many senators were Democrat and how many were Republican?

Answer 1

Let the number of republicans be

`r`

Let the number of democrats be

`d`

For a recent Congress, there were 10 more Democrats than Republicans in the U.S. Senate.

This can be represented below as

`d=r+10`

The ratio of democrats to republicans is

`(d)/(r)=(11)/(9)`

put d=r+10

`\begin{gathered} (d)/(r)=(11)/(9) \\ (r+10)/(r)=(11)/(9) \\ cross\text{ multiply} \\ 11r=9(r+10) \\ 11r=9r+90 \\ 11r-9r=90 \\ 2r=90 \\ (2r)/(2)=(90)/(2) \\ r=45 \end{gathered}`

Substitute r =45 in the equation belo

`\begin{gathered} d=r+10 \\ d=45+10 \\ d=55 \end{gathered}`

Hence,

The final answer is

55 democrats

45 republicans