Question

The U.S. Senate has 100 members. After a certain election, there were 8 more Democrats

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

Answer 1

• 54 Democrats
• 46 Republicans

Explanation:

You want to know the number in each party if the total is 100 and there are 8 more Democrats than Republicans.

Setup

Let d represent the number of Democrats. Then d-8 is the number of Republicans. The total is ...

d +(d -8) = 100

Solution

Simplifying gives ...

2d -8 = 100

2d = 108

d = 54

d-8 = 54 -8 = 46

There were 54 Democrats and 46 Republicans.

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