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 24 more votes in favor than against, with three times as many Democrats voting in favor as non-Democrats voting in favor, and with 33 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
Republicans
other parties
members
members
members
Need Help?
Read It
Submit Answer
Home MyAssignments

Step 1 ：Given that in the 75th Congress (1937-1939) there were in the Senate 75 Democrats, 17 Republicans, and 4 members of other parties. A bill passed the Senate with 24 more votes in favor than against, with three times as many Democrats voting in favor as non-Democrats voting in favor, and with 33 more Democrats voting in favor than Republicans voting in favor. If every member voted either for the bill or against it, we are to find how many Democrats, how many Republicans, and how many members of other parties voted in favor of the bill.

Step 2 ：Let's denote the number of Democrats who voted in favor as \(D\), the number of Republicans who voted in favor as \(R\), and the number of others who voted in favor as \(O\).

Step 3 ：From the problem, we can set up the following system of equations:

Step 4 ：1. The total number of votes in favor is 24 more than the votes against. Since every member voted, the total votes is the total number of members, which is 75 Democrats + 17 Republicans + 4 others = 96. So, the votes in favor is \((96 + 24) / 2 = 60\), and the votes against is \((96 - 24) / 2 = 36\). This gives us the equation \(D + R + O = 60\).

Step 5 ：2. Three times as many Democrats voted in favor as non-Democrats. This gives us the equation \(D = 3 * (R + O)\).

Step 6 ：3. There are 33 more Democrats voting in favor than Republicans. This gives us the equation \(D = R + 33\).

Step 7 ：Solving this system of equations, we find that \(D = 45\), \(R = 12\), and \(O = 3\).

Step 8 ：Final Answer: The number of Democrats, Republicans, and members of other parties who voted in favor of the bill are \(\boxed{45}\), \(\boxed{12}\), and \(\boxed{3}\), respectively.