In a town, 80% of the men are registered voters and 66% of the women a

Question

In a town, 80% of the men are registered voters and 66% of the women are registered voters. if 78% of the total population is a registered voter, what fraction of the population is Men?

A. 72/100
B. 78/100
C. 80/100
D. 82/100
E. 86/100

Archit3110 · Accepted Answer

let total size of population be 100
so out of 78 which is the registered voter population men and women voter be x & y 
so
0.8x+0.66y=78
and x+y=100

solve for x & y we get , x= 86 and y = 14
so men population is 86/100 or 86% IMO E

generis · Answer

Use a weighted average to find the ratio of men to women. The ratio will yield the fraction of the total who are men.

M = # of men 
W = # of women
% = fraction of each group who are registered voters
%(M+W) = fraction of total population who are registered voters =  \frac{78}{100}

(% M)(M) + (% W)(W) = %(M+W) * (M+W)

\frac{80}{100}M+\frac{66}{100}W=\frac{78}{100}(M+W)

80M+66W=78M+78W

2M=12W

Ratio of men to women  \frac{M}{W}=\frac{12}{2}=\frac{6}{1}

For every 6 men there is 1 woman. Men are what fraction of the population?

\frac{M}{M+W}=\frac{6}{6+1}=\frac{6}{7}=.857\approx.86

M\approx\frac{86}{100}  of the population

Answer E

dave13 · Answer

total population = t woman = w men = m m+w =t w = t-m plug into equation below 80m+66w = 78t 80m+66(t-m) = 78t 80m+66t-66m = 78t 80m-66m = 78t-66t 14m = 12t if we are asked ratio men to total population then logically it should be \frac{14m}{12t} but it doesnt look like correct answer but if i reverese it then i get E but in this case i dont get logic

can anyone explain whats wrong with my reasoning - highlighted part

may be like this

14m = 12t now to find m I divide by 14 m = \frac{12t}{14}

but T is total population !!!

Gladiator59 maybe you can explain one detail. look I got 14m = 12t (m = means men and t = total population) to find ratio of men to total population I divide by 14 by both sides and get 12t/14 BUT t is total population why is it in numerator shouldn't it be vice versa 14m/12t can you please explain

ShankSouljaBoi · Answer

M/T =12/14 = 6/7 That is the answer.
Again , 6/7 =.86 = 86/100

See, you were just there !!

Posted from my mobile device

Gladiator59 · Answer

dave13 , You have done correct calculations. Let me help you get the logic of 14m = 12t

If t was 100, whatever m would be, it would represent the percentage of men.
m = 12/14 * 100 = 6/7 * 100 or E.

Hope this makes sense. The fraction of total represents percent.

Best,
GLadi

KarishmaB · Answer

Responding to a pm:

Using scale method, assuming w1 is the weight of men and w2 is the weight of women,

w1/w2 = (A2 - Aavg)/(Aavg - A1)

w1/w2 = (66 - 78)/(78 - 80) = 6/1

Men form 6/7 of the population which is (6/7)*100 = approx 86%

Answer (E)

Swanoff · Answer

Bunuel  this question is easy to solve but fraction and percentage values don't match. Otherwise it should be written as "approximately what fraction of voters are men ? "

In a town, 80% of the men are registered voters and 66% of the women a

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In a town, 80% of the men are registered voters and 66% of the women a

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