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The problem of the convention

The problem of the convention



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“Mr. President,” said the secretary, the call for a vote in which the attendees who supported the motion were to stand was approved with a difference of votes equal to one third of the opposition's components.

Since the result obtained was due to the lack of chairs to allow eleven members to sit down who could not register their negative vote, we are informed that the proposal has actually been rejected by a difference of one vote.

Can you tell me what is the number of votes actually cast at this meeting?

Solution

There were 147 votes cast in total. In the first round the affirmative vote won with a ratio of 4 to 3 (84 to 63) with respect to the negative vote but when eleven votes were transferred from the affirmative side to the negative, in the negative there was a majority of one (84 - 11 = 73 against 63 + 11 = 74).

This shows that 21 was a seventh of the total number of votes.