There are 810 male and female participants in a meeting. Half the female participants and one-quarterof 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) 135  E) 225
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 810.   Hence, we have m+f= 810   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 = 810/3= 
<gadget id="calculator">810/3</gadget>
<output>270</output>
270   Solving the three equations yields the solution   f= 270,m= 540, and d= 270.   The number of female democratic participants equals half the female participants equals   270/2= 
<gadget id="calculator">270/2</gadget>
<output>135</output>
135.   ANSWER:135
<result>D</result>
There are 810 male and female participants in a meeting. Half the female participants and one-quarterof the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female?