Let x = number of children in group 2
then x + 50 = number of children in group 1
we are given that the sum of the two groups is 300
so, 300 = x + x +50
300 - 50 = 2x
250 = 2x
125 = x
so, group 2 has 125 children, and group 1 has 125 + 50 = 175 children
And, 125 + 175 = 300