Unity Eternity

Number Theory Level pending

In a mixed company consisting of Poles, Turks, Greeks, Germans and Italians. The Poles are one less than one third of the number of the Germans, and three less than the half of the number of Italians. The Turks and Germans outnumber the Greeks and Italians by three; the Greeks and Germans form one less than half the company; while the Italians and the Greeks form seven-sixteenths of the company.

Determine number of each nation.

Note: Write your solution as sum of numbers of all nations.

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