Another party

Let Total no. of people at party is x. Then as per given we have
x/2+x/3+15=x which result x=90

Let the number of people at the party be $n$ . Then, the number of people who drank lemonade was $\frac {1}{2} n$ and cola, $\frac {1}{3} n$ . The remaining 15 people who drank nothing was:

$n - \frac {1}{2} n - \frac {1}{3} n = 15 \quad \Rightarrow \left( \dfrac {6-3-2}{6} \right) n = \frac {1}{6} n = 15\quad \Rightarrow n = 15\times 6 = \boxed{90}$

Let's use geometry. Half means $\frac{180}{360}$ , if we plus $\frac{1}{3}$ = $\frac{300}{360}$

$360-300 = 15p$

$p = 60/15 = 4$

$\frac{360}{4} =$ $90$

x/2 +x/3+15=x , as x is an assumption for total no. of people in the party. this on further calculation gives x=90.

Let $p = people$ , $l = Lemonade$ and $c = Cola$

Half of the party goers drank only lemonade so

$l = \frac {p}{2}$

Only a third drank cola so

$c = \frac {p}{3}$

And $15$ drank neither. From this information we get the equation

$l + c + 15 = p$

Since $l = \frac {p}{2}$ and $c = \frac {p}{3}$ we can substitute them in

$(\frac {p}{2}) + (\frac {p}{3}) + 15 = p$

Cross multiplying the two fractions gives us

$\frac {5p}{6} + 15 = p$

Re-arrange it to get $p$

$p - 15 = \frac {5p}{6} \Rightarrow 6p - 90 = 5p \Rightarrow p - 90 = 0 \Rightarrow p = 90$

The amount of people at the party was $90$