Set the number of participants in the contest *** there are x people, then the number of people who won the first prize is 1/12 x people, the number of people who won the second prize is
1/9 x people, according to the meaning of the question to get
1/12x + 1/9x = 35
The solution is x = 180
Answer: *** there are 180 people to participate in the contest.