Question

At a recent election a total of 93648 votes were cast for the 4 candidates, the winner exceeding his opponents by 25627, 10681 and 55924 votes respectively . How many votes cast for each candidate?

Answer 1

The number of votes cast for each candidate are as follows:

Candidate a = 46470

Candidate b = 20843

Candidate c = 35789

Candidate d = -9454

Explanation:

Let A, B, C and D represents the number of votes for a (winner), b, c and d candidates. Therefore, we have:

A + B + C + D = 93648 ................. (1)

Also, we have:

A - B = 25627

B = A - 25627 ........ (2)

A - C = 10681

C = A - 10681 ............. (3)

A - D = 55924

D = A - 55924............. (4)

Substituting equations (2), (3) and (4) into (1) and solve for A, we have:

A + A - 25627 + A - 10681 + A - 55924 = 93648

4A = 93648 + 25627 + 10681 + 55924

4A = 185880

A = 185880 / 4

A = 46470

Substituting A = 46470 into each of equations (2), (3) and (4), we have:

B = 46470 - 25627 = 20843

C = 46470 - 10681 = 35789

D = 46470 - 55924 = -9454

Therefore, the number of votes cast for each candidate are as follows:

Candidate a = 46470

Candidate b = 20843

Candidate c = 35789

Candidate d = -9454

Additional Note:

It should be noted that Candidate d has negative votes of -9454. This is possible because a negative vote is voting system that gives votes the opportunity to indicate dislike for a candidate, without increasing the votes of other candidates, and the number of dislikes will be the number of votes that will be deducted from the votes of the candidates. Therefore, a candidate can have negative votes cast if he gets only dislikes or more dislikes than votes.