In a tennis club, there are twice as many male members as female members. 1/3 of the males wear hats when they play. 1/4 of the females wear hats when they play. 66 members wear hats. How many members does the club have?

Let m be the number of males. Let f be the number of females.
(1/3)m + (1/4)f = 66      (1)
m = 2f                   (2)
(1/3) * 2f + (1/4)f = 66  (substitute (2) into (1))
(2/3)f + (1/4)f = 66
(8/12)f + (3/12)f = 66
(11/12)f = 66
f = 66 / (11/12)
f = 66 * (12/11)
f = 66 * (1 + (1/11))
f = 66 + 66 * (1/11)
f = 66 + 6
f = 72                     (3)
m = 2 * 72                 (substitute (3) into (2))
m = 144
total number of members = 72 + 144 = 216