Question

In a study of bat migration habits, $240$ male bats and $160$ female bats have been tagged. If $100$ more female bats are tagged, how many more male bats must be tagged so that $\frac{3}{5}$ of the total number of bats in the study are male?

Answer 1

Once the $100$ additional female bats are tagged, you’ll have $240$ males and $260$ females $—$ a total of $500$ bats.

Every male bat you tag adds not only to the number of male bats, but also to the total number of tagged bats. Your current male to total ratio is $\frac{240}{500}$.

Let the number of male bats added be $x$

Then , $\frac{3}{5}=\frac{240+x}{500+x}$

$\Rightarrow 3(500+x)=5(240+x)$

$\Rightarrow 1500+3x=1200+5x$

$\Rightarrow 300=2x$

$\Rightarrow x=150$

Hence, $150$ more male bats must be tagged.