58 people attended an art competition and were given some coloring tubes. Each child received 6 tubes and each adult received 3 tubes. All children received 186 more tubes than all adults. How many adults attended the competition?

Answer 1

Let's assume that the number of children attending the competition is c and the number of adults is a.
From the information given, we have two equations:
1) c + a = 58 - the total number of people attending the competition is 58
2) 6c = 3a + 186 - the total number of tubes given to children is 186 more than the tubes given to adults
Multiplying the second equation by 2 and subtracting the first equation from it, we get 12c - 2c = 6a - 2a + 372 - 2(58)
Simplifying the equation, we get 10c = 4a + 256
From equation 10c = 4a + 256, we can deduce that the number of adults (a) must be divisible by 4 and end in 0.
The only value that satisfies those conditions is a = 40.
Substituting this value into equation 1), we find: c + 40 = 58
Therefore, c = 58 - 40 = <<58-40=18>>18
So, there were 18 children and 40 adults attending the competition. Answer: \boxed{40}.