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Puzzle Details

A rich aristocrat decided that he would give every man 45 dollars and every woman 60 dollars.

Only one ninth of the men and only one twelfth of the women collected their dues.

Can you tell me how much money the aristocrat spent if there were 3552 people in total?

Puzzle Copyright © Kevin Stone

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Answer: 17,760 dollars.

If there were M men, then there were (3552 - M) women.

So one ninth of the men each received 45 dollars and one twelve of the women each received 60 dollars. So the total received was:

= 45 x 1 x M  +  60 x  1 x (3552 - M)
       -              --
       9              12

Simplify the two fractions by dividing the 45 by 9, and the 60 by 12 respectively.

= 5 x M + 5 x (3552 - M)

= 5M + 17760 - 5M

= 17760

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