# The ratio of men to women working for a company is 7 to 4. If there are 189 men working for the company, what is the total number of employees?

Nov 6, 2016

$189$ men and $108$ women.

Total number is $297$

#### Explanation:

Start by using ratio form to write down what is given:

$\text{ }$men : women
$\text{ } 7 : 4$
" "189: ?

Now determine the relationship between $7 \mathmr{and} 189$

$\text{ }$men : women
$\text{ } 7 : 4$

$\textcolor{red}{\times 27} \downarrow$

" "189: ?

Do exactly the same for the women.

$\text{ }$men : women
$\text{ } 7 : 4$

 color(red)(xx27)darr""darrcolor(red)(xx27)

$\text{ } 189 : 108$

Total number = $189 + 108 = 297$

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You can also use direct proportion:

$\frac{7}{4} = \frac{189}{x} \text{ } \leftarrow$ cross multiply

$7 x = 4 \times 189$

$x = \frac{4 \times 189}{7}$

Number of women: $x = 108$

Total number = $189 + 108 = 297$

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However, in both cases you can find the total number in one step.
$7 + 4 = 11 \text{ } \leftarrow$ find 11 parts.

$\text{ }$men : total
$\text{ } 7 : 11$

 color(red)(xx27)darr""darrcolor(red)(xx27)

$\text{ } 189 : 297$

Total number $= 297$#

OR

$\frac{7}{11} = \frac{189}{x} \text{ } \leftarrow$ cross multiply

$7 x = 11 \times 189$

$x = \frac{11 \times 189}{7}$

Total number = $297$