Question 264699
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Let *[tex \Large f] represent the number of females.  Let *[tex \Large m] represent the number of males.  Presuming that all 8000 residents are either male or female and there are no other unaccounted for possibilities, we can say:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ f\ +\ m\ =\ 8000]


Which we will find convenient later to express as:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ m\ =\ 8000\ -\ f]


Since no one married more than once, and presuming all of the marriages were the traditional two-person man/woman arrangements, one-sixth of the females must be equal in number to one-fourth of the males, that is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{f}{6}\ =\ \frac{m}{4}]


Cross-multiplying, we obtain


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4f\ =\ 6m]


Using the modified version of our first equation, make the substitution for *[tex \Large m], thus:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4f\ =\ 6\left(8000\ -\ f\right)]


Now all you have to do is solve for *[tex \Large f]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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