Question

It was recently estimated that females outnumber males by about three or two. If there are 1770 people in a county, how many of them are females?

Answer 1

GIVEN

1) Females outnumber males by 3 to 2.

2) There are 1770 people in the city.

SOLUTION

Let the number of males be x and the number of females y. Therefore, the total number of people can be written to be:

`x+y=1770\text{ -----------(1)}`

If there are 3 females for every 2 males, we have that:

`\begin{gathered} (y)/(3)=(x)/(2) \\ \therefore \\ x=(2y)/(3)\text{ ----------(2)} \end{gathered}`

We can substitute equation (2) into equation (1) and solve for y:

`\begin{gathered} (2)/(3)y+y=1770 \\ (2y+3y)/(3)=1770 \\ 5y=1770*3 \\ 5y=5310 \end{gathered}`

Dividing both sides by 5, we have

`y=1062`

There are 1062 females in the county.