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October 19th, 2015, 12:05 AM  #1 
Newbie Joined: Oct 2015 From: Pakistan Posts: 1 Thanks: 0  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? 
October 19th, 2015, 04:14 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 
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. 
October 19th, 2015, 05:18 AM  #3  
Senior Member Joined: Apr 2014 From: Europa Posts: 571 Thanks: 176  Quote:
$\displaystyle \scriptsize\color{blue} {m = the\ number\ of\ men \\ \\ w= the\ number\ of\ women \\\;\\m+w = 84\ \ \ (1) \\ \\ w=\dfrac{m}{2}\ \Longrightarrow\ \dfrac{m}{2} = w \Longrightarrow\ w = 2m\ \ \ (2) \\\;\\ (1),\ (2) \ \Longrightarrow\ 2w+w = 84\ \Longrightarrow\ 3w = 84 \ \Longrightarrow\ w = 84:3 \ \Longrightarrow\ w = 28\ \ \ (3) \\ \\ (2),\ (3) \ \Longrightarrow\ m=2\cdot28\ \Longrightarrow\ m = 56\ \ \ (4) \\\; \\ The\ next\ month,\ we\ have: \\ \\ w' = 28+8\ \Longrightarrow\ w' = 36\ \ \ (5) \\ \\ \dfrac{w'}{m'}=\dfrac{3}{4}\ \stackrel{(5)}{\Longrightarrow}\ \dfrac{36}{m'} = \dfrac{3}{4}\ \Longrightarrow\ m' = \dfrac{36\cdot4}{3} =12\cdot4 \ \Longrightarrow\ m'=48\ \ \ (6) \\ \\ (4),\ (6)\ \Longrightarrow\ 5648=8 \ men \ left.}$  
October 19th, 2015, 05:31 AM  #4 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,445 Thanks: 2499 Math Focus: Mainly analysis and algebra 
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".

October 19th, 2015, 05:48 AM  #5  
Senior Member Joined: Apr 2014 From: Europa Posts: 571 Thanks: 176  Quote:
It can be a point of view, even for the man at the door.  
October 19th, 2015, 07:19 AM  #6 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 616 Thanks: 82  I understand your point, but I'm assuming whoever wrote the question was looking for the net change in number of men.

October 19th, 2015, 04:32 PM  #7 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,878 Thanks: 1087 Math Focus: Elementary mathematics and beyond 
"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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the ratio of male and female members of a club is 5:6 the ratio wil be reserved if 22 female members leave the club. the number if male member is,at a local country club with 84 members there are half as many woman
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