Question
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
Answers
Answered by
GPT 3.5
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.
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.