Trial and improvement:

K is even
As they are children they won't be that old

Let K=2
S=1
T=0 doesn't work

Let K=4
S=2
T=3
B=1 but total of boys does not equal total of girls

Let K=6
S=3
T=5
B=3 but total of boys does not equal total of girls

Let K=8
S=4
T=7
B=5 total of boys does equal total of girls

Algebraically:

Algebraically

B=T-2	(I)
T+B = K+S	(II)
K=2S	(III)
T-1 = 2(S-1) T= 2S -1	(IV)
T+T-2=2S+S	From(I II III)
2T - 2 = 3S
(4S - 2) -2 = 3S	Sub for T from (IV)
S=4
K=8	From (III)
T=7	From (IV)
B=5	From (I)