If an election, there were two candidates. One of them received 65% of the votes casted and scored a majority of 1500 votes more than its competitor. How many people casted the votes?


Let the total number of votes cast be \( x \).

One candidate received 65% of the votes, so the number of votes they received is:
\[
0.65x
\]

The other candidate received the remaining 35% of the votes, so the number of votes they received is:
\[
0.35x
\]

The candidate who received 65% of the votes won by a majority of 1500 votes, which means:
\[
0.65x - 0.35x = 1500
\]

Simplifying the left-hand side:
\[
0.30x = 1500
\]

Now, solve for \( x \):
\[
x = \frac{1500}{0.30} = 5000
\]

So, the total number of votes cast is **5000**.

Would you like more details on any step or have any questions?

Here are 5 related questions to deepen your understanding:

1. What if the majority had been 2000 votes? How would that change the total number of votes cast?
2. If 10% of the votes were declared invalid, how many valid votes were cast?
3. How would the problem change if the majority were given as a percentage instead of a specific number?
4. What if three candidates contested the election? How would you approach the problem?
5. How would the solution change if 55% of the votes were required to win the election?

**Tip**: Always convert percentages into decimal form when working with them in algebraic equations for clarity and accuracy.

If an election, there were two candidates. One of them received 65% of the votes casted and scored a majority of 1500 votes more than its competitor. How many people casted the votes?

Learn how to solve an election problem where a candidate receives 65% of the votes and has a majority of 1500 votes. This problem covers key algebraic concepts and percentage calculations. Suitable for students in Grades 9-10.

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