Question

In a state legislature, there were 1119 more members in the House of Representatives than in the Senate. If the total number of members in both houses is 256, how many members are in the Senate?

Answer 1

The mathematical problem as stated leads to an impossible solution for the number of Senate members, suggesting there might be a typo or error in the provided numbers. Typically, the Senate, as a part of the U.S. Congress, has a fixed number of 100 members.

Step-by-step explanation:

The student is asking how many members are in the Senate given that there were 1119 more members in the House of Representatives and the total number of members in both houses is 256. To solve this problem, let us denote the number of Senate members as S and the number of House members as H. We have two pieces of information:

1. There were 1119 more House members than Senate members, so H = S + 1119.
2. The total number of members in both houses is 256, so H + S = 256.

By substituting the first equation into the second, we get:

S + 1119 + S = 256

Combining like terms, we get:

2S + 1119 = 256

Subtracting 1119 from both sides, we find:

2S = 256 - 1119

2S = -863

Dividing both sides by 2, we get:

S = -431.5

However, since the number of Senate members cannot be negative or a fraction, there appears to be a discrepancy in the question as it may contain a typo or the given numbers may be incorrect. In the context of the U.S. political system which the question may implicitly refer to, each state has exactly two senators, for a total of 100 senators.