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The U.S. Senate has 100 members. After a certain election, there were 12 more Democrats than Republicans, with no other parties represented. How many members of each party were there in the Senate?

◻ Democrats

◻ Republicans
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The U.S. Senate has $100$ members. After a certain election, there were $12$ more Democrats than Republicans, with no other parties represented. How many members of each party were there in the Senate? $\newline$ $\square$ Democrats $\newline$ $\square$ Republicans $\newline$ View an example $\newline$ Get more help $\cdot$ $\newline$ Clear all $\newline$ Check answer

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Experiment design

Full solution

Q. The U.S. Senate has

100

members. After a certain election, there were

12

more Democrats than Republicans, with no other parties represented. How many members of each party were there in the Senate?

\newline

\square

Democrats

\newline

\square

Republicans

\newline

View an example

\newline

Get more help

\cdot

\newline

Clear all

\newline

Check answer

Define Variables: Let's call the number of Democrats $D$ and the number of Republicans $R$ . We know that $D = R + 12$ because there are $12$ more Democrats than Republicans.
Total Senate Members: We also know that the total number of Senate members is $100$ . So, we can write the equation $D + R = 100$ .
Substitute in Equation: Substitute $D$ with $R + 12$ in the equation from the previous step to get $(R + 12) + R = 100$ .
Combine Like Terms: Now, combine like terms: $2R + 12 = 100$ .
Isolate Term with R: Subtract $12$ from both sides to isolate the term with R: $2R = 100 - 12$ .
Solve for R: Do the subtraction: $2R = 88$ .
Calculate R: Divide both sides by $2$ to solve for R: $R = \frac{88}{2}$ .
Find Democrats: Calculate $R$ : $R = 44$ . So, there are $44$ Republicans.
Calculate D: Now, use the first equation $D = R + 12$ to find the number of Democrats: $D = 44 + 12$ .
Calculate D: Now, use the first equation $D = R + 12$ to find the number of Democrats: $D = 44 + 12$ .Calculate D: $D = 56$ . So, there are $56$ Democrats.

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