In an election x got 30% more votes than Y and Z got 25% more votes than Y. X overtook Z by 5000 votes. Only 71% people voted and no invalid votes. Find no. Of people in voter list.

Let's denote the number of votes for Y as \( y \).

### Given information:
1. \( x \) got 30% more votes than \( y \), so \( x = 1.3y \).
2. \( z \) got 25% more votes than \( y \), so \( z = 1.25y \).
3. \( x \) overtook \( z \) by 5000 votes, meaning \( x - z = 5000 \).
4. Only 71% of the people in the voter list voted, and there were no invalid votes.

### Step 1: Set up the equation for votes difference between \( x \) and \( z \):
\[
x - z = 5000
\]
Substituting the values of \( x \) and \( z \) from the above relationships:
\[
1.3y - 1.25y = 5000
\]
Simplifying:
\[
0.05y = 5000
\]
\[
y = \frac{5000}{0.05} = 100,000
\]
Thus, the number of votes for \( y \) is 100,000.

### Step 2: Calculate the votes for \( x \) and \( z \):
- \( x = 1.3 \times 100,000 = 130,000 \)
- \( z = 1.25 \times 100,000 = 125,000 \)

### Step 3: Calculate the total number of votes:
The total number of votes cast is the sum of the votes for \( x \), \( y \), and \( z \):
\[
\text{Total votes} = x + y + z = 130,000 + 100,000 + 125,000 = 355,000
\]

### Step 4: Determine the total number of people in the voter list:
Since only 71% of the people in the voter list voted:
\[
0.71 \times \text{Voter list} = 355,000
\]
\[
\text{Voter list} = \frac{355,000}{0.71} = 500,000
\]

Thus, the total number of people in the voter list is **500,000**.

---

Would you like more details or have any questions?

### Related questions:
1. How would the problem change if 80% of people had voted instead of 71%?
2. What if the difference in votes between \( x \) and \( z \) was 10,000 instead of 5,000?
3. How can you verify that there were no invalid votes in an election scenario?
4. What would the outcome be if \( x \) had received 40% more votes than \( y \)?
5. How does voter turnout impact the calculation of total voters in an election?

### Tip: 
In election-based problems, always express relationships between candidates using percentages and then convert them into algebraic equations for easier solving.

In this problem, you will calculate the total number of people in a voter list where X, Y, and Z receive votes with different percentage increases. Learn to set up algebraic equations and solve using percentages. Suitable for Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation