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?

Question

32137 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-06T12:01:53

$189$ men and $108$ women.

Total number is $297$

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

$" "$ men : women
$" "7:4$
$" "189: ?$

Now determine the relationship between $7 and 189$

$" "$ men : women
$" "7:4$

$color(red)(xx27)darr$

$" "189: ?$

Do exactly the same for the women.

$" "$ men : women
$" "7:4$

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

$" "189: 108$

Total number = $189+108 = 297$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
You can also use direct proportion:

$7/4 = 189/x" "larr$ cross multiply

$7x = 4 xx189$

$x = (4xx189)/7$

Number of women: $x = 108$

Total number = $189+108 = 297$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
However, in both cases you can find the total number in one step.
$7+4=11" "larr$ find 11 parts.

$" "$ men : total
$" "7:11$

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

$" "189: 297$

Total number $= 297$ #

OR

$7/11 = 189/x" "larr$ cross multiply

$7x = 11 xx189$

$x = (11xx189)/7$

Total number = $297$