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October 19th, 2015, 12:05 AM   #1
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ratio

plz provide solution of this question

At a local country club with 84 members,
there are half as many women as there are
men. The next month, 8 women join and the
ratio of women to men is now 3 to 4. How
many men joined or left?
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October 19th, 2015, 04:14 AM   #2
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Don't you at least want to try to do it yourself? You learn more by doing than by watching someone else do it!

Let "M" be the number of men in the country club to begin with, "W" the number of women.

"At a local country club with 84 members,"
So M+ W= 84.

"there are half as many women as there are men."
So W= M/2.

"The next month, 8 women join"
So now there are W+ 8 women.

"and the ratio of women to men is now 3 to 4. How
many men joined or left? "
Let the number of men who joined or left be "x" (If men left then x will be negative.)
There are now M+ x men and W+ 8 women so the "ratio of women to men" is now
$\displaystyle \frac{W+ 8}{M+ x}= \frac{3}{4}$

You have three equations, W+ M= 84, W= M/2, and [tex]\frac{W+8}{M+ x}= \frac{3}{4}[/itex] to solve for W, M, and x- though you only need to find x.

(If you don't like fractions, W= M/2 is the same as 2W= M and $\displaystyle \frac{W+ 8}{M+ x}= \frac{3}{4}$ is the same as 4(W+ 8 )= 3(M+ x) so 4W+ 32= 3M+ 3x.)

(It is easy to solve the first two equations alone for M and W. If M= 2W then W+ M= 84 becomes W+ 2W= 3W= 84 so W= 84/3= 28 and M= 84- 28= 56.)

Last edited by Country Boy; October 19th, 2015 at 04:19 AM.
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October 19th, 2015, 05:18 AM   #3
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Quote:
Originally Posted by sunnyarain View Post
plz provide solution of this question

At a local country club with 84 members,
there are half as many women as there are
men. The next month, 8 women join and the
ratio of women to men is now 3 to 4. How
many men joined or left?


$\displaystyle \scriptsize\color{blue} {m = the\ number\ of\ men
\\ \\
w= the\ number\ of\ women
\\\;\\m+w = 84\ \ \ (1)
\\ \\
w=\dfrac{m}{2}\ \Longrightarrow\ \dfrac{m}{2} = w \Longrightarrow\ w = 2m\ \ \ (2)
\\\;\\
(1),\ (2) \ \Longrightarrow\ 2w+w = 84\ \Longrightarrow\ 3w = 84 \ \Longrightarrow\ w = 84:3 \ \Longrightarrow\ w = 28\ \ \ (3)
\\ \\
(2),\ (3) \ \Longrightarrow\ m=2\cdot28\ \Longrightarrow\ m = 56\ \ \ (4)
\\\; \\
The\ next\ month,\ we\ have:
\\ \\
w' = 28+8\ \Longrightarrow\ w' = 36\ \ \ (5)
\\ \\
\dfrac{w'}{m'}=\dfrac{3}{4}\ \stackrel{(5)}{\Longrightarrow}\ \dfrac{36}{m'} = \dfrac{3}{4}\ \Longrightarrow\ m' = \dfrac{36\cdot4}{3} =12\cdot4 \ \Longrightarrow\ m'=48\ \ \ (6)
\\ \\
(4),\ (6)\ \Longrightarrow\ 56-48=8 \ men \ left.}$
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October 19th, 2015, 05:31 AM   #4
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The question is not answerable, because some men may have joined and some women may have left. It is only answerable if "a net total of 8 women joined" and we are required to find "the net total number of men who joined/left".
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October 19th, 2015, 05:48 AM   #5
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Quote:
Originally Posted by v8archie View Post
The question is not answerable, because some men may have joined and some women may have left. It is only answerable if "a net total of 8 women joined" and we are required to find "the net total number of men who joined/left".

It can be a point of view, even for the man at the door.
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October 19th, 2015, 07:19 AM   #6
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Quote:
Originally Posted by v8archie View Post
The question is not answerable, because some men may have joined and some women may have left. It is only answerable if "a net total of 8 women joined" and we are required to find "the net total number of men who joined/left".
I understand your point, but I'm assuming whoever wrote the question was looking for the net change in number of men.
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October 19th, 2015, 04:32 PM   #7
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"half as many women as there are men" implies 3w = 84, with w the number of women, so there were 28 women. "8 women join" so the number of women is then 36. 36/48 = 3/4 and there were 56 men so 8 men left.
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