SOLUTION: The ratio of men to women at a certain company is 5 to 7. How many male employees does the company have if there are 204 employees?

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Question 329639: The ratio of men to women at a certain company is 5 to 7. How many male employees does the company have if there are 204 employees?

Found 2 solutions by jim_thompson5910, Edwin McCravy:
Answer by jim_thompson5910(35256) About Me  (Show Source):
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Let x = number of male employees and y = number of female employees


So because "there are 204 employees", this means that x%2By=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%2F7=x%2Fy (basically the ratio of 'x' men to 'y' women is 5 to 7)


5%2F7=x%2Fy Start with the given equation.


5%2F7=x%2F%28204-x%29 Plug in y=204-x


5%28204-x%29=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=%28-1020%29%2F%28-12%29 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.

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
The ratio of men to women at a certain company is 5 to 7. How many male employees does the company have if there are 204 employees?
Us this rule:
If x things and y things are in a ratio of a to b, then in a group of x+y things, x = %28a%28x%2By%29%29%2F%28a%2Bb%29 and y = %28b%28x%2By%29%29%2F%28a%2Bb%29

Here, x male employees and y female employees are in a ratio of 5 to 7, so in this group of x+y, or 204 people, x = %285%28204%29%29%2F%285%2B7%29%22%22=%22%221020%2F12%22%22=%22%2285 and y = %287%28204%29%29%2F%285%2B7%29%22%22=%22%221428%2F12%22%22=%22%22119. [Or we could have just found one of them,
and found the other by subtracting from 204.]
Edwin