Matches played between boys and girls

Let $g_j$ and $b_j$ be the number of girls and boys in the junior level, where $g_j + b_j = 43$. Girl vs girl matches in junior level: $\binom{g_j}{2} = 153 \implies g_j(g_j - 1) = 306 = 18 \times 17$. So $g_j = 18 \implies b_j = 43 - 18 = 25$.

Let $g_s$ and $b_s$ be the number of girls and boys in the senior level, where $g_s + b_s = 51$. Boy vs boy matches in senior level: $\binom{b_s}{2} = 276 \implies b_s(b_s - 1) = 552 = 24 \times 23$. So $b_s = 24 \implies g_s = 51 - 24 = 27$.

Matches played between a boy and a girl occur within juniors and within seniors: In juniors: $b_j \times g_j = 25 \times 18 = 450$. In seniors: $b_s \times g_s = 24 \times 27 = 648$.

Total boy vs girl matches $= 450 + 648 = 1098$.