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:

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

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

$\begin{gathered} \frac{2}{3}y+y=1770 \\ \frac{2y+3y}{3}=1770 \\ 5y=1770\times3 \\ 5y=5310 \end{gathered}$

Dividing both sides by 5, we have

$y=1062$

There are 1062 females in the county.