Fund Raiser

Let $x$ be the number of men and $y$ the number of women. We can set up a diophantine equation: $67x + 59y = 4978$

By Euclidean algorithm, we can calculate:

$67= 59 + 8$

$59 = 8•7+3$

$8= 3•2+2$

$3= 2•1+1$

Then $1= ( 59-8•7)-(8-3•2)= 59•25-22•67$

Thus, $4978= 59(25•4978)-67(22•4978)$ .

That is, $x_{0} = -22•4978$ and $y_{0}=25•4978$ .

Since $67$ and $59$ are coprime, $x= x_{0}+59n >0$ and $y=y_{0}-67n>0$ .

Hence, $\dfrac{25•4978}{67}>n>\dfrac{22•4978}{59}$ .

Only $n=1857$ works.

As a result, $x=-22•4978+59•1857=47$ .

$y=25•4978-67•1857=31$ .

Finally, the total benefactors= $47+31=\boxed{78}$ .