5 In an election, 35% of the voters voted for candidate P whereas 50% of the remaining
voted for candidate Q. The remaining voters did not vote. If the difference between
those who voted for candidate P and those who did not vote was 1000, the number of
individuals eligible for casting a vote in that election was:


Let's define the total number of eligible voters as \( V \).

Given:
- 35% of the voters voted for candidate P.
- 50% of the remaining voters voted for candidate Q.
- The remaining voters did not vote.
- The difference between those who voted for candidate P and those who did not vote is 1000.

First, let's find the number of voters who voted for candidate P:
\[ \text{Voters for P} = 0.35V \]

The number of remaining voters after P's votes:
\[ \text{Remaining voters} = V - 0.35V = 0.65V \]

Out of these remaining voters, 50% voted for candidate Q:
\[ \text{Voters for Q} = 0.5 \times 0.65V = 0.325V \]

The remaining voters who did not vote:
\[ \text{Non-voters} = 0.65V - 0.325V = 0.325V \]

We are given that the difference between those who voted for candidate P and those who did not vote is 1000:
\[ 0.35V - 0.325V = 1000 \]

Simplify the equation:
\[ 0.025V = 1000 \]

Solving for \( V \):
\[ V = \frac{1000}{0.025} \]
\[ V = 40000 \]

Thus, the number of individuals eligible for casting a vote in that election was \( 40,000 \).

Would you like further details or have any questions?

Here are 5 questions you might want to ask:
1. How do you set up equations based on word problems?
2. What are common percentages problems in elections and voting scenarios?
3. How do you solve for an unknown variable in algebraic equations?
4. Can you provide more examples of solving word problems with percentages?
5. What are the steps to simplify algebraic expressions?

Tip: When dealing with word problems, carefully translate the text into mathematical expressions, step by step, to ensure accuracy in setting up and solving equations.

Learn how to calculate the total number of eligible voters in an election using percentages and algebraic equations. This problem involves finding the total number of voters, voters for candidate P, voters for candidate Q, and those who did not vote, with a detailed step-by-step solution. Suitable for students in Grades 9-12.

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