Let X represents the male participants in a meeting.
Let Y represents the female participants in a meeting.
Given: X + Y = 750. - (A)
Third statement in the question: 1 / 3 of all the participants are Democrats
which implies (1 / 3) multiplied by 750 = 250.
This means: the total number of DEMOCRATS= 250.
Also given: Half the female participants and 1 / 4 of male are Democrats.
This implies: (X / 4) + (Y / 2) = 250
Therefore, X + 2Y = 1000 - (B)
Now Subtracting (A) from (B) implies: X + 2Y - X -Y = 1000 - 750
Y = 250
This represents - The total number of the female participants in a meeting are 250. According to the given statement above half the female participants are DEMOCRATS. 125 Democrats are female.