Personal Comment: Hard one for Christmas!

Christmas Bonus Enigma

Story: A company offered its 350 employees a Christmas bonus of $10 to each male and $8.15 to each female. All the females accepted, but a cetain percentage of the males refused to accept. The total bonus paid was not dependent upon the number of men employed.

Enigma: What was the total amount paid to the women?

Solution Let m be the number of men and let x be the fraction of men refusing a bonus. Then the amount paid out is given by
T=8.15(350-m)+10(1-x)m=2852.50+m(1.85-10x)
which will be independent of m only if x=0.185, so that T=2852.50. Both m and 0.185m are integers with m _ 350, so m=200. It follows that $1,222.50 is paid to the 150 women.

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