30 junior and 42 senior participants participate in a tournament. Each pair of juniors plays one match, and each pair of seniors plays one match. Number of boys versus boys matches in juniors is 105, while the number of girls versus girls matches in seniors is 210. If total number of matches played between participants of different genders is (7n + 57), then find the value of 'n'.

Let the number of boys in junior be 'x'.

^xC2 = 105

Or, x(x - 1) ÷ 2 = 105

Or, x² - x - 210 = 0

Or, x² - 15x + 14x - 210 = 0

Or, x(x - 15) + 14(x - 15) = 0

Or, (x - 15)(x + 14) = 0

So, 'x' = 15 or 'x' = -14

But 'x' cannot be negative. So, 'x' = 15

Number of boys in junior = 15

Number of girls in junior = 30 - 15 = 15

Let the number of girls in senior be 'y'.

yC2 = 210

Or, y(y - 1) ÷ 2 = 210

Or, y² - y - 420 = 0

Or, y² - 21y + 20y - 420 = 0

Or, y(y - 21) + 20(y - 21) = 0

Or, (y - 21)(y + 20) = 0

So, 'y' = 21 or 'y' = -20

But 'y' cannot be negative. So, 'y' = 21

Number of girls in senior = 21

Number of boys in senior = 42 - 21 = 21

Required number of matches = 15 × 15 + 21 × 21 = 225 + 441 = 666

7n + 57 = 666

Or, 7n = 609

Or, n = 87