Election Mathematics: Solving Complex Voting Scenarios with SEO-Friendly SEO Techniques

In the realm of democratic processes, understanding election outcomes requires a clear mathematical approach. This article outlines step-by-step problem-solving techniques using an example involving two candidates, uncast and invalid votes, and victory margins.

Problem Setup

Let's consider the following scenario: There are two candidates in an election, and we are given the following information:

10,000 voters did not cast their votes. 75% of the cast votes are valid. The winning candidate won by 2,250 votes. The losing candidate received 18% of the total votes.

Our task is to determine the total number of votes cast in the election. Let's solve this step-by-step.

Solution

Step 1: Define Variables

Let ( x ) be the total number of votes cast in the election. We need to express the number of valid votes and the votes for each candidate in terms of ( x ).

Step 2: Calculate Valid Votes

Since 10,000 voters did not cast their votes, the number of cast votes is ( x - 10,000 ). Given that 75% of the cast votes are valid, the number of valid votes is:

[ 0.75(x - 10,000) ]

Step 3: Votes for Each Candidate

Let's denote the number of votes for the winning candidate as ( W ) and the number of votes for the losing candidate as ( L ). We know:

[ L 0.18x ]

The winning candidate won by 2,250 votes, so:

[ W L 2,250 0.18x 2,250 ]

Step 4: Total Valid Votes

The total valid votes must equal the number of votes for the winning and losing candidates combined:

[ W L 0.75(x - 10,000) ]

Substituting ( W ) and ( L ):

[ (0.18x 2,250) 0.18x 0.75(x - 10,000) ]

Simplify and solve for ( x ):

[ 0.36x 2,250 0.75x - 7,500 ]

[ 0.39x 9,750 ]

[ x 25,000 ]

This step-by-step approach confirms that the total number of votes cast in the election is 39,000.

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