## Task 1 - 170711

Matthias was in an international pioneer tent camp during the summer holidays. He reports to his classmates:

"A quarter of all participants and four pioneers came from the Soviet Union, a fifth of all participants and five pioneers from the GDR, a sixth of all participants and six pioneers from Czechoslovakia, an eighth of all participants and eight pioneers from the People's Republic of Poland, a ninth of all participants and nine pioneers from the People's Republic of Bulgaria. The remaining 21 pioneers came from the Hungarian People's Republic. In each tent of the camp, there were exactly eight pioneers."

Determine the number of tents in the camp from these details!
Let \( x \) be the number of all participants. According to the problem, we have:

\[
x = \left(\frac{1}{4} x + 4\right) + \left(\frac{1}{5} x + 5\right) + \left(\frac{1}{6} x + 6\right) + \left(\frac{1}{8} x + 8\right) + \left(\frac{1}{9} x + 9\right) = 21
\]

from which we obtain \( x = 360 \).

Since \( 360 \div 8 = 45 \), the number of tents was thus 45.