SOLUTION: The U.S. Senate has 100 members. After a certain​ election, there were 18 more Democrats than​ Republicans, with no other parties represented. How many members of each

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Question 1126568: The U.S. Senate has 100 members. After a certain​ election, there were 18 more Democrats than​ Republicans, with no other parties represented. How many members of each party were there in the​ Senate?
Answer by sbro7568(4)   (Show Source): You can put this solution on YOUR website!
To represent the number of Democrats in the Senate, we will use the variable D. For Republicans, we will use R.
If there are 18 more Democrats than Republicans, we can create an equation for the number of Democrats: .
If there are 100 members in total, an equation for the total could be .
If we plug in the first equation to the second equation to replace D, we can . When we simplify this equation, we get . We can then subtract 18 from both sides to get , then divide both sides by 2 and get . Therefore, since R represents the number of Republicans, there are 41 members of that party in the Senate.
To get the number of Democrats, we can plug in 41 to the first equation we created, to get . When we simplify this, we get . Therefore, there are 59 Democrats in the Senate.
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tl;dr:
Democrats = 59
Republicans = 41
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