There are 750 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 choice from the following answers: A) 150 B) 135 C) 160 D) 125 E) None
Explanation :   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 750.   Hence, we have m+f= 750   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   =&gt; d = 750/3= 
<gadget id="calculator">750/3</gadget>
<output>250</output>
250   Solving the three equations yields the solution=&gt; f = 250,m= 500, and d= 250.   The number of female democratic participants equals half the female participants equals   =&gt; 250/2= 
<gadget id="calculator">250/2</gadget>
<output>125</output>
125.   Hence (D) is the correct answer.   Answer : 125
<result>D</result>
There are 750 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?