Question 329639
Let x = number of male employees and y = number of female employees



So because "there are 204 employees", this means that {{{x+y=204}}}. Solve for y to get {{{y=204-x}}}



Also, since "The ratio of men to women at a certain company is 5 to 7", this means that {{{5/7=x/y}}} (basically the ratio of 'x' men to 'y' women is 5 to 7)



{{{5/7=x/y}}} Start with the given equation.



{{{5/7=x/(204-x)}}} Plug in {{{y=204-x}}}



{{{5(204-x)=7x}}} Cross multiply



{{{1020-5x=7x}}} Distribute.



{{{-5x=7x-1020}}} Subtract {{{1020}}} from both sides.



{{{-5x-7x=-1020}}} Subtract {{{7x}}} from both sides.



{{{-12x=-1020}}} Combine like terms on the left side.



{{{x=(-1020)/(-12)}}} Divide both sides by {{{-12}}} to isolate {{{x}}}.



{{{x=85}}} Reduce.



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Answer:


So the solution is {{{x=85}}} 



So this means that the company has 85 male employees.