There are 840 male and female participants in a meeting. Half the female participants and one-quarter of the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female?
Choose the correct answer.
A) 75  B) 100  C) 125  D) 140  E) 225

Rationale: "let m be the number of male participants and f be the number of female articipants in the meeting . thetotal number of participants is given as 840 . hence , we have m + f = 840 now , we have that half the female participants and one - quarter of the male participants are democrats . let d equal the number of the democrats . then we have the equation f / 2 + m / 4 = d now , we have that one - third of the total participants are democrats . hence , we have the equation d = 840 / 3 = 280 solving the three equations yields the solution f = 280 , m = 560 , and d = 280 . the number of female democratic participants equals half the female participants equals 280 / 2 = 140 . answer : d"
Answer: D