There were initially 75 kids at camp, and 21 kids went swimming. So, there are 75 - 21 = 54 kids remaining. The counselor separated these remaining kids into 6 teams, each with k kids. We can set up an equation to find the value of k:
6 * k = 54
Now, divide both sides by 6:
k = 54 / 6
k = 9
So, the value of k is 9. The counselor put 9 kids into each of the 6 teams.