# Out of the original girls and boys at a carnival party 40% of the girls and 10% of the boys left early, 3/4 of them decided to hang out and enjoy the festivities. There were 18 more boys than girls in the party. How many girls were there to begin with?

Oct 4, 2016

If I have interpreted this question correctly, it describes an impossible situation.

#### Explanation:

If $\frac{3}{4}$ stayed then 1/4=25% left early

If we represent the original number of girls as $\textcolor{red}{g}$
and the original number of boys as $\textcolor{b l u e}{b}$

color(white)("XXX")40% xxcolor(red) g + 10% xx color(blue)(b) = 25% xx (color(red)g+color(blue)b)

$\textcolor{w h i t e}{\text{XXX}} \rightarrow 40 \textcolor{red}{g} + 10 \textcolor{b l u e}{b} = 25 \textcolor{red}{g} + 25 \textcolor{b l u e}{b}$

$\textcolor{w h i t e}{\text{XXX}} \rightarrow 15 \textcolor{red}{g} = 15 \textcolor{b l u e}{b}$

$\textcolor{w h i t e}{\text{XXX}} \rightarrow \textcolor{red}{g} = \textcolor{b l u e}{b}$

...BUT we are told $\textcolor{b l u e}{b} = \textcolor{red}{g} + 18$