How can we calculate the total number of votes cast in an election where 2% of voters didn't participate, 500 votes were invalid, and one candidate received 43% of the votes while defeating the other by 200 votes?
By TecScholar
Let's solve a problem step by step where an election result is analyzed based on given conditions.
Problem
In an election, 2% of registered voters did not participate, and 500 votes were invalid. Candidates A and B contested the election, and A defeated B by 200 votes. If 43% of registered voters voted for A, find the total number of votes cast.
Solution
- Let the total number of registered voters = x.
- Voters who participated = 98% of x, i.e., 0.98x.
- Invalid votes = 500. Therefore, valid votes = 0.98x - 500.
- Candidate A defeated B by 200 votes. Thus, A's votes = B's votes + 200.
- 43% of registered voters voted for A. Hence, A's votes = 0.43x.
Equations:
Total valid votes:
A's votes + B's votes = 0.98x - 500
Substitute A's votes = B's votes + 200:
(B's votes + 200) + B's votes = 0.98x - 500
Simplify:
2(B's votes) + 200 = 0.98x - 500
B's votes = 0.49x - 350
From A's votes = 0.43x:
A's votes + B's votes = 0.98x - 500
0.43x + (0.49x - 350) = 0.98x - 500
Solve for x:
0.06x = 150
x = 2500
Result:
Total votes cast = 0.98x = 0.98 × 2500 = 2450.
Answer: 2450 votes were cast.
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