Balloon distribution

Algebra Level 3

During a party, the host distributed balloons to his guests in this way:
He gave the first guest 2 balloons plus \(\frac{1}{9}\) of the remainder;
the second guest 4 balloons plus \(\frac{1}{9}\) of the remainder;
the third guest 6 balloons plus \(\frac{1}{9}\) of the remainder;
the first fourth 8 balloons plus \(\frac{1}{9}\) of the remainder;
and so on, until the last guest got the final remainder.

If all the guests got an equal number of balloons, how many guests were there and how many balloons did each guest get?

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