Question

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?

Answer 1

`189` men and `108` women.

Total number is `297`

Explanation:

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`