Answered

Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Get immediate and reliable answers to your questions from a community of experienced experts on our platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

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?

Sagot :

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

Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.