jmc

Let $a$ denote the number of chocolate candies, $b$ the number of vanilla, $c$ the number of peppermint, and $d$ the number of lemon. We can represent the information given in the problem with the following system of linear equations: $$\begin{array}{rl}a+b+c+d& =15\\ 2(a+b)& =c+d\\ c-8& =d\end{array}$$ Substituting for $c+d$ in terms of $a+b$ into the first equation gives $3a+3b=15$, or $a+b=5$. This means that $c+d=10$. The third equation can also be expressed as $c-d=8$. Adding these two equations gives $2c=18$, so $c=9$. Because $d=c-8$, $d=\boxed{1}$.