In an election there were four candidate,5/6 of the electors voted for the winner.The runner up received 4/7 of the remaining votes.The third candidates received twice the vote of the fourth candidate.if the winner received 3021 votes more than the runner up ,how many electors voted
Let the total number of electors be x.
1st candidate (winner) received (5/6)*x votes
Remaining votes = x - (5/6)*x = (1/6)*x
2nd candidate (runner up) received (4/7)*(1/6)*x votes
3rd candidate received 2 times the votes of 4th candidate, so 3rd candidate received 2*(1/6)*x votes and 4th candidate received (1/6)*x votes.
Given that the winner received 3021 votes more than the runner up, we can write the equation:
(5/6)*x = (4/7)*(1/6)*x + 3021
Multiplying both sides by 42 to eliminate the fractions:
35x = 4x + 127482
Subtracting 4x from both sides:
31x = 127482
Dividing both sides by 31:
x = 4110
Therefore, the total number of electors who voted is 4110.
Let's represent the number of electors who voted as "x".
According to the information given:
- 5/6 of the electors voted for the winner.
- The runner-up received 4/7 of the remaining votes, which means 1 - 5/6 = 1/6 of the electors did not vote for the winner.
- The third candidate received twice the vote of the fourth candidate.
Let's calculate step-by-step:
1. The number of electors who voted for the winner: (5/6) * x.
2. The number of electors who did not vote for the winner: (1/6) * x.
3. The number of votes received by the runner-up: (4/7) * (1/6) * x.
4. The number of votes received by the third candidate: 2 * (4/7) * (1/6) * x.
5. The number of votes received by the fourth candidate: (4/7) * (1/6) * x.
6. The difference between the votes of the winner and the runner-up: (5/6) * x - (4/7) * (1/6) * x = 3021.
Now we can solve the equation:
(5/6) * x - (4/7) * (1/6) * x = 3021.
To simplify the equation, we can multiply through by the least common denominator of 6 and 7, which is 42:
(35/42) * x - (4/42) * x = 3021.
Simplifying further:
(35x - 4x) / 42 = 3021.
31x / 42 = 3021.
Cross-multiplying:
31x = 42 * 3021.
31x = 126582.
Dividing both sides by 31:
x = 126582 / 31.
Calculating x:
x ≈ 4080.06.
Since the number of electors must be a whole number, approximately 4080 electors voted in the election.