Three candidates contested a students' union election and every vote cast was valid. The winner polled 42% of the votes, the runner-up 33% and the third candidate the rest. The winner beat the runner-up by 1800 votes. How many students voted?

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Accepted Answer

20000. The margin is 42 − 33 = 9% of the votes cast, so 0.09T = 1800 → T = 20000. (The three candidates then polled 8400, 6600 and 5000.) Dividing 1800 by 0.42 or by 0.33 answers a question nobody asked — the margin belongs to the DIFFERENCE of the two shares, not to either share on its own.

Three candidates contested a students' union election and every vote cast was valid. The winner polled 42% of the votes, the runner-up 33% and the third candidate the rest. The winner beat the runner-up by 1800 votes. How many students voted?

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