(i)

Let n = number of individuals who like basketball.

F = {Individuals who like football}

B = {Individuals who like basketball}

Number of individuals who like football = 3 x n = 3n

Number of individuals who like both games = $\frac{1}{3}$ x n = $\frac{\mathrm{n}}{3}$

(ii)

Coverying F

3n + n - $\frac{\mathrm{n}}{3}$ + 139 = 1382

Get rid of the fraction by multiplying both sides by the denominator 3.

3 x 3n + 3 x n - $\frac{\mathrm{n}}{3}$ x 3 + 139 x 3 = 1382 x 3

9n + 3n - n + 417 = 4146

11n = 4146 - 417

11n = 3729

Divide both sides by 11

n = $\frac{3729}{11}$ = 339