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?
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}.
Let "c" represent the number of children attending the competition and "a" represent the number of adults attending the competition.
We know that each child received 6 tubes and each adult received 3 tubes. Therefore, the total number of tubes given to children is 6c and the total number of tubes given to adults is 3a.
According to the given information, the total number of tubes given to children is 186 more than the total number of tubes given to adults. Mathematically, this can be expressed as:
6c = 3a + 186
We also know that the total number of attendees at the competition is 58. Therefore, we can write another equation using this information:
c + a = 58
We now have a system of two equations:
6c = 3a + 186
c + a = 58
We can solve this system of equations to find the values of "c" and "a".
Let's first solve the second equation for c:
c = 58 - a
Now substitute this value of "c" into the first equation:
6(58 - a) = 3a + 186
Expand and solve for "a":
348 - 6a = 3a + 186
-6a - 3a = 186 - 348
-9a = -162
a = 18
Therefore, there were 18 adults attending the art competition.