In a state where I do not tell you how many voters are, after counting 60 % of the votes, candidate A got 55 % of the counted votes. What % of the uncounted votes does she need to win?

To find out what percentage of the uncounted votes candidate A needs to win the election, we can break down the problem step by step.

### Let's define:
- **\( T \)**: Total number of votes.
- **\( C \)**: Votes already counted (which is 60% of total votes, so \( C = 0.6T \)).
- **\( U \)**: Votes uncounted (which is 40% of total votes, so \( U = 0.4T \)).
- **\( V_A \)**: Votes candidate A has received so far.
- **\( V_B \)**: Votes candidate B has received so far.

### Given:
- Candidate A has received 55% of the counted votes, so \( V_A = 0.55C = 0.55(0.6T) = 0.33T \).

### Candidate A needs more than 50% of the total votes to win:
- Total votes needed to win: \( 0.5T \).

### Let \( X \) be the percentage of uncounted votes that candidate A needs:
- The total number of votes candidate A will have after counting all votes is:
  \[
  V_A + X \times U = 0.33T + X \times 0.4T
  \]
- For candidate A to win, this total should be greater than 50% of the total votes:
  \[
  0.33T + X \times 0.4T > 0.5T
  \]
- Subtract \( 0.33T \) from both sides:
  \[
  X \times 0.4T > 0.5T - 0.33T
  \]
  \[
  X \times 0.4T > 0.17T
  \]
- Divide both sides by \( 0.4T \):
  \[
  X > \frac{0.17T}{0.4T} = \frac{0.17}{0.4} = 0.425
  \]

### Conclusion:
Candidate A needs to secure **42.5%** of the uncounted votes to win the election.

Would you like to see the detailed breakdown of any steps? Here are some related questions:

1. How do percentages work in election scenarios?
2. How can we calculate the remaining votes a candidate needs to win?
3. What happens if the percentage required to win changes?
4

Learn how to calculate the percentage of uncounted votes candidate A needs to win the election. This problem involves understanding percentages, proportions, and solving equations. Suitable for high school students and anyone interested in election mathematics.

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