Question: 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?

Posted by: arushi on 30.12.2017

Let m be the number of male participants and f be the number of female participants in the meeting. The total 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 d = 750/3 = 250 Solving the three equations yields the solution f = 250, m = 500, and d = 250. The number of female democratic participants equals half the female participants equals 250/2 = 125

Let no of females be x & no of males be y.

x + y = 750 -------- (1)

x/2 + y/4 = 750/3

2x + y = 1000 --------- (2)

From (1)& (2),

x = 250

No. female democrats = x/2 = 250/2 = 125

Female = x Male = 750-x x/2 + 750-x/4 = 1/3* (750)= 250 x= 250 x/2 = 125

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.

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