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The elections

The elections

Here I present a problem that arose in recent elections in which 5,219 votes were cast for four candidates. The winner took his opponents an advantage of 22, 30 and 73 votes, and no one knew how to find out the exact number of votes received by each.

Can you give a rule to find out?

Solution

Add the advantages to the total number of votes and divide it by the number of candidates, the quotient will be the number of votes of the winner, from which the votes of the other candidates can be determined by subtracting them.

The votes will be 1,336, 1,314, 1,306 and 1,263.