Question

In the 75th Congress (1937−1939) there were in the Senate 75 Democrats, 17 Republicans, and 4 members of other parties. Suppose that a bill passed the Senate with 16 more votes in favor than against, with three times as many Democrats voting in favor as non-Democrats voting in favor, and 30 more Democrats voting in favor than Republicans voting in favor. If every member voted either for the bill or against it, how many Democrats, how many Republicans, and how many members of other parties voted in favor of the bill?
Democrats members
Republicans members
other parties members

Answer 1

Answer:

42 Democrats members

12 Republicans members

2 other parties members

Step-by-step explanation:

We know that there are a total number of voters of

• 75 (democrats)+17 (Republicans)+ 4( Other parties)=  96 voters

And we know that the bill has passed with 16 nore votes in favor that against, so let's calculate how many votes in favor of the bill we have:

• 96 Votes = F (votes in Favor)+ A (votes against)

also: F= A+16= A = F-16, so:

• 96= F+A= F+F-16 => F= 56 votes in favor of the bill

Thos 56 votes are the sum of the votes in favor from all the parties:

56 = D (votes in favor of democrats)+R ((votes in favor of Republicans)+OTH (votes in favor of other parties)

=> 56= D+R+OTH (A)

also democrat's votes in favor are three times the sum of non-democrat's votes in favor:

• D= 3*( R+OTH) => OTH= D/3-R

and we have 30 more democrats thar republicans voting in favor:

• D= R+30 => R=D-30

if we replace in the (A) formula:

56 = D+R+OTH => 56= D+D-30+D/3-D+30 =>

• 56=4/3*D => D=42 (DEMOCRATS VOTES IN FAVOR)
• R= D-30 => R= 12 (REPUBLICAN VOTES IN FAVOR)
• OTH= D/3-R= 14-12= 2 (OTHER PARTIE'S VOTES IN FAVOR)