Answer:
32 rounds.
Step-by-step explanation:
A putt putt course offers a deal that when you purchase 10 rounds of gold you get 1 round for free.
10 + 1 = 11 rounds On every 11 round there is 1 free round
you played a total of 35 rounds.
This means you played 
= 3.1 ≈ 3 times of 11 rounds + 2 rounds
in 3 times of 11 round, you purchased 30 rounds and got 3 free rounds plus 2 more round.
Since total round 35 rounds = 35 = 3(10 rounds) + 3 free rounds + 2 more rounds
Therefore, you purchased 30 + 2 = 32 rounds and got 3 free rounds.