There are 1143 members in a club. 5/6 of the women and 3/7 of the men in the club volunteered to help out at an elderly home. There were 672 volunteers.
(a) How many men volunteered at the elderly home?
(b) What fraction of the members were women? Express your answer in the simplest form.
+166 Let's say that there are \(6x\) women, and \(7y\) men. So then, \(5x\) women volunteered and \(3y\) men volunteered.
From this, we have the system of equations
\(6x+7y=1143\)
\(5x+3y=672\)
Solving, we get \(x=75\) and \(y=99\).
(a) Since \(y=99\), we know that there were \(3\cdot99=\boxed{297}\) male volunteers.
(b) Since \(x=75\), there were \(6\cdot75=450\) women, so then \(\frac{450}{1143}=\boxed{\frac{50}{127}}\) of the members were women.
