Can you help me understand the answer to this question? At a Halloween party, there are 30 guests, 16 of whom are Draculas and 14 of whom are Mummies. Assuming no Mummies leave, how many Draculas need to arrive to make the ratio of Draculas to guests 2:3? The answer is 12 Draculas, but I don't get where that number comes from.
Thanks.
On
16 is the current value of draculas, 14 the current value of mummies. So all in all its the number of guests. If you divide the number of vampires by the number of vampires and the number of mummies, which is the number of guests, you end up with a ratio. So $ \frac{16}{16+14}=\text{some_ratio} $. The job is now to change the number of vampires by x, so we end up with the following.
$$ \frac{16+x}{16+x+14} = \frac{2}{3} $$
Set up your problem as
$$\frac{D+x}{G+x}=\frac23$$
Where $D$ is the initial number of Draculas, $G$ is the initial number of guests, and $x$ is how many more Draculas enter the party.