Question

In a tournament, there are 43 junior level and 51 senior level participants. Each pair of juniors play one match. Each pair of seniors play one match. There is no junior versus senior match. The number of girl versus girl matches in junior level is 153, while the number of boy versus boy matches in senior level is 276. The number of matches a boy plays against a girl is

Answer 1

Correct Answer: 1098

Total Number of Boy-Girl Matches in Junior and Senior Groups 

Junior Group

Let the number of girls be \( n \). Total matches among girls is given as:

\[ \frac{n(n-1)}{2} = 153 \Rightarrow n(n - 1) = 306 \Rightarrow n = 18 \]

Hence, number of boys in Junior group:

\[ 43 - 18 = 25 \]

Matches between boys and girls in Junior group:

\[ 25 \times 18 = 450 \]

Senior Group

Let the number of boys be \( n \). Matches among boys:

\[ \frac{n(n - 1)}{2} = 276 \Rightarrow n(n - 1) = 552 \Rightarrow n = 24 \]

Hence, number of girls in Senior group:

\[ 51 - 24 = 27 \]

Matches between boys and girls in Senior group:

\[ 27 \times 24 = 648 \]

Total Boy-Girl Matches

\[ 450 + 648 = \boxed{1098} \]