BTGmoderatorLU wrote:In a certain state, the ratio of registered Republicans to registered Democrats is 3 to 2, and every registered voter is either a Republican or a Democrat. If 80 percent of the Republicans and 15 percent of the Democrats are expected to vote for Candidate X, and everyone else is expected to vote for Candidate Y, by what percent is Candidate X expected to win the election?

A. 2%
B. 5%
C. 8%
D. 10%
E. 15%

We are given that the ratio of Republicans to Democrats = 3x : 2x, so the total number of voters is 5x.

Since 80 percent of the Republicans and 15 percent of the Democrats are expected to vote for Candidate X:

0.8(3x) = 2.4x Republicans and 0.15(2x) = 0.3x Democrats are expected to vote for Candidate X.

So, Candidate X receives 2.4x + 0.3x = 2.7x votes out of 5x votes, and the other candidate, Candidate Y, receives 5x - 2.7x = 2.3x votes.

Therefore, Candidate X will win by:

(2.7x - 2.3x)/5x = 0.4/5 = 4/50 = 8%.

Alternate Solution:

Let's assume that there are 30 republicans and 20 democrats in this state.

The candidate X will receive 80% of the republican votes, which is 30*(0.8) = 24 votes and 15% of the democrat votes, which is 20*(0.15) = 3 votes. In total, the candidate X receives 24 + 3 = 27 of the 50 votes; which is equivalent to 54% of all the votes.

Since candidate X receives 54% of the votes, candidate Y will receive 100 - 54 = 46% of all the votes and candidate X will win by 54 - 46 = 8%.

Answer: C