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## 'Mathland Election' printed from http://nrich.maths.org/

On Mathland TV a political commentator summed up an election
result as follows.

A Labour majority of $1729$ last time has been turned
into a Conservative majority of $1654$ in this election and the
conservative candidate has obtained $38\%$ of the poll. Labour has
taken second place. The Liberal Democrat has obtained only $14\%$
of the poll and has been beaten into fourth place by the SNP
candidate who has $50$ more votes than the Liberal
Democrat.

Given that there were just four candidates and that the figures
quoted were exact find the number of votes polled for each
candidate.

[This question comes from the book 'Mathematical Challenges'
published in 1989 for the Scottish Mathematical Council by Blackie,
ISBN 0216 92622X]