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The problem asks us to determine how many voters supported candidate B two weeks before the final survey, given the data about voter transitions between candidates A and B.

### Key information:
1. In the final survey:
   - 1230 voters support candidate A.
   - 980 voters support candidate B.

2. Voter movement between surveys:
   - 5.2% of voters who supported candidate A in the previous survey now support candidate B.
   - 4.4% of voters who supported candidate B in the previous survey now support candidate A.

We can set up the following system to track the votes two weeks before the final survey:

Let:
- \( A_{-2} \) be the number of voters who supported candidate A two weeks before the final survey.
- \( B_{-2} \) be the number of voters who supported candidate B two weeks before the final survey.

From the movement rates:
- 5.2% of \( A_{-2} \) moved from A to B: \( 0.052 \times A_{-2} \).
- 4.4% of \( B_{-2} \) moved from B to A: \( 0.044 \times B_{-2} \).

The net result of the movement must match the final survey numbers:
\[
A = A_{-2} - 0.052 \times A_{-2} + 0.044 \times B_{-2} = 1230
\]
\[
B = B_{-2} - 0.044 \times B_{-2} + 0.052 \times A_{-2} = 980
\]

I will now solve this system to find \( B_{-2} \), the number of voters who supported candidate B two weeks before the final survey.The number of voters who supported candidate B two weeks before the final survey is approximately **957** (rounded to the nearest integer).

Would you like more details or have any questions? Here are 5 related questions to consider:

1. How do small changes in percentages affect voter dynamics in surveys?
2. What methods can be used to model transitions between choices in surveys over time?
3. How would different transition rates (percentages) change the final result?
4. How can we use systems of equations to solve problems involving movement between two groups?
5. What assumptions might affect the accuracy of these types of survey predictions?

**Tip:** When solving systems of equations, double-check your model's assumptions to ensure they match real-world conditions, especially if percentages or movement between categories are involved.

In the final survey before the elections, 1230 voters say that they will vote for candidate A and 980 voters say that they will vote for candidate B. How many of the voters answered that they would vote for candidate B in the survey that was conducted two weeks before the final survey?

Discover how to calculate voter transitions between candidates A and B in local election surveys using algebraic systems of equations. Understand key concepts and formulas related to voter dynamics. Suitable for Grades 10-12 students.

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