Election Voters Calculation Explained

Let $E$ denote the total number of enrolled voters.

1. Valid Votes Calculation

The candidate secured $9261$ votes, representing $75\%$ of the total valid votes ($V_{valid}$).

We set up the equation:

$9261 = 0.75 \times V_{valid}$

To find the number of valid votes, we solve for $V_{valid}$:

$V_{valid} = \frac{9261}{0.75} = \frac{9261}{3/4} = 9261 \times \frac{4}{3} = 12348$

So, there were $12348$ valid votes.

2. Total Votes Cast Calculation

The $12348$ valid votes represent $98\%$ of the total votes cast ($V_{cast}$), because $2\%$ of the votes cast were invalid ($100\% - 2\% = 98\%$).

The relationship is:

$12348 = 0.98 \times V_{cast}$

Solving for $V_{cast}$:

$V_{cast} = \frac{12348}{0.98} = \frac{12348}{98/100} = 12348 \times \frac{100}{98} = 12600$

Thus, $12600$ votes were cast in total.

3. Enrolled Voters Calculation

We know that $75\%$ of the total enrolled voters ($E$) cast their votes. We found that $12600$ votes were cast ($V_{cast}$).

The equation is:

$12600 = 0.75 \times E$

Solving for the total enrolled voters ($E$):

$E = \frac{12600}{0.75} = \frac{12600}{3/4} = 12600 \times \frac{4}{3} = 16800$

Final Answer: Total Enrolled Voters

The total number of voters enrolled in the election was $16800$.