Question

In an election, a candidate received 55% of the total votes and won by a margin of 600 votes. How many votes were cast in total?

Answer 1

Let the total number of votes cast be denoted as \( V \). According to the problem, the candidate received 55% of the total votes, which can be expressed as:

\[
\text{Votes for candidate} = 0.55V
\]

The other candidate, therefore, received the remaining percentage of the votes, which is:

\[
\text{Votes for other candidate} = V - 0.55V = 0.45V
\]

The problem states that the candidate won by a margin of 600 votes. This margin can be expressed as the difference between the votes received by the two candidates:

\[
\text{Margin} = \text{Votes for candidate} - \text{Votes for other candidate} = 0.55V - 0.45V
\]

This simplifies to:

\[
\text{Margin} = 0.10V
\]

Given that the margin is also 600 votes, we can set up the equation:

\[
0.10V = 600
\]

To find \( V \), divide both sides of the equation by 0.10:

\[
V = \frac{600}{0.10} = 6000
\]

Thus, the total number of votes cast in the election is:

\[
\boxed{6000}
\]

Answer 2

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