how many Democrats, how many Republicans, and how many members of other parties voted in favor of the bill?

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 40 more votes in favor than against, with three times as many Democrats voting in favor as non-Democrats voting in favor, and 38 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?

Answer 1

Let D= number Democrats voting for, R=Republicans for and O=other parties voting for

D=3(R+O)=3R+3O 3 times as many Democrats vote for as non-Democrats

D=38+R 38 more Democrats vote for as Republicans

38+R=3R+3O

2R=38-3O

R=19-3O/2

total votes 75+17+4=96 96 minus votes for = votes against

O=4 or 3 or 2 or 1 or 0 Try O=4 first

for O=4, R=13 and D=38+13=51

(D,R,O) = (51, 13, 4) is the solution

The bill passed with 40 more in favor than against

for (51,13,4) 51+13+4=68 voted for and 96-68=28 voted against 68-28=40 more in favor than against

This question was prior to when Alaska and Hawaii became states, so there were only 96 Senators, not 100.