37. Overtime Work. A certain company offered 350 of its employees to work overtime, with each man being offered a reward of 10 dollars, and each woman - 8 dollars and 15 cents. All women agreed to this offer, while some men refused. Upon calculation, it was found that the total reward amount does not depend on the number of male employees. What is the total reward amount paid to all women?
37. Let $m$ be the total number of men, and $x$ be the fraction of men who refused to work overtime. Then the total amount of compensation paid is

$$
T=8.15(350-m)+10(1-x) m=2852.50+m(1.85-10 x)
$$

which is independent of $m$ only if $x=0.185$. It is also known that $m<350$ and that both $m$ and $0.185 m$ are integers. Therefore, $m=200$. From this, it follows that 150 women received a total compensation of 1220 dollars and 50 cents. 

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