Question 1014745
Let m = # of men who attended, w = # of women who attended, and c = # number of children who attended.

Then 
m + w + c = 120, and
5m + 2w + 0.10c = 120.

Substituting c = 120 - m - w into the second equation, we get

5m + 2w + 0.10(120 - m - w) = 120, which, after simplifying, gives

4.9m + 1.9w = 108, or

49m + 19w = 1080. This becomes a Diophantine problem, and as such requires (non-negative) integer solutions.

By brute force, we obtain m = 17 and w = 13, from which we get c = 90.
(These values can also be obtained using the Euclidean algorithm.)

Thus, there were 17 men, 13 women, and 90 children.