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# Math

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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.

Jun 11, 2022

#1
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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.

Jun 11, 2022
#2
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M + W =   1143       →    1143 - W  = M       (1)

(3/7)M + (5/6)W =  672      (2)

Sub   (1) into (2)

(3/7) ( 1143 - W)  + (5/6)W =  672

Solving for W  produces    450 = W

So  (b)  =      450 /1143 =  50 / 127

And

a)   M =   1143 - 450 =   693

So  (3/7) (  693)  =    297  M   volunteered   Jun 11, 2022
edited by CPhill  Jun 11, 2022