In a society of 550 people, there are three types of cars liked: A, B, and C. The ratio of people who like car A to car C is 29 : 42 29 : 42 29 : 42 ....

In a society of 550 people, there are three types of cars liked: A, B, and C. The ratio of people who like car A to car C is $29 : 42$. The number of people who like only car A and car C together is one-fourth of those who like only car B. The number of people who like only car C is 50 more than four times the number of people who like only car A and B together. Ten people like all three types of cars, which is equal to the number of people who like only car B and C together. The number of people who like only car C is twice the number of people who like only car A. The total number of people who like car C is 210. Everyone likes at least one of the three cars. How many people do not like any of the three cars?