Question

the ratio of men to women working for a company is 3 to 5. if there are 216 employees total, how many men work for the company?

Answer 1

`81\:\text{men}`

Explanation:

Since there are 3 men for every 5 women in the company, for each women there will be
`(3)/(5)` men.

Therefore, we can write the following system of equations:

`\begin{cases}(3)/(5)w=m,\\w+m=216\end{cases}`

Solving, we get:

`w+(3)/(5)w=216,\\(8)/(5)w=216,\\w=216\cdot (5)/(8)=135\:\text{women}`

Therefore, there are
`216-135=\boxed{81\:\text{men}}` in the company.