Question

It was recently estimated that females outnumber males by about three to two. If there are 1760 people in a county, how many of them are females?

Answer 1

The problem says that there's a proportion between females and males, and this proportion is 3:2, for 3 females there are 2 males.

That means that if we divide the people into 5 equal parts, 3 parts will be female and 2 parts will be male.

Using that logic, let's divide the county people into 5 equal parts

`(1760)/(5)=352`

Then each part has 352 people. As we said, 3 parts will be female, then

`\begin{gathered} f=352\cdot3 \\ \\ f=1056 \end{gathered}`

Therefore, there are 1056 females.

And the males will be 2 parts, then

`\begin{gathered} m=352\cdot2 \\ \\ m=704 \end{gathered}`

We can also check that the males + females must be all the population:

`\begin{gathered} p=m+f \\ p=704+1056 \\ p=1760 \end{gathered}`

Again, there are 1056 females in the county