SOLUTION: Hi 2/7 of the members in a country club are men. 1050 women in the club are below 50 years old. If there are 960 more women than men in the club, how many women are above 50 yea

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Question 1097282: Hi
2/7 of the members in a country club are men.
1050 women in the club are below 50 years old.
If there are 960 more women than men in the club, how many women are above 50 years old.
thanks
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
(2/7)t=m
(5/7)t=w
w=m+960
b=1050
How many women who are exactly 50 is not given!
Assuming that above and below 50 include all women we have:
w=b+a
(2/7)t=m
(5/7)t=w
w=m+960
m=w-960
b=1050
we need to solve for a
w=b+a
w=1050+a
a=w-1050
t=m+w
t=w-960+w
t=2(1050+a)-960
t=2100+2a-960
t=1140+2a
t/2-570=a
(5/7)t=w
t=7/5*w
t=w-960+w
7/5*w=2w-960
7/5=2-960/w
960/w=2-7/5
960/w=10/5-7/5
960/w=3/5
960*5/3=w
1600=w
w=1050+a
1600=1050+a
1600-1050=a
a=550 women over 50
Done but for fun we find the total in the club and the number of men
t=7/5*1600
t=2240 total club members
m=t-w
m=2240-1600=640
640 are men
1600 are women
check
m+960=1600
640+960=1600
(2/7)t=m
(2/7)*2240=m
m=640
(5/7)t=w
(5/7)*2240=w
w=1600
ok