jmc

Call the number of red marbles $a$, the number of yellow marbles $b$, the number of orange marbles $c$, and the number of white marbles $d$. We can express the information given in the problem by the following system of linear equations: $$\begin{array}{rl}a+b+c+d& =35\\ \frac{a}{2}=b-2=\frac{c}{3}& =\frac{d+3}{3}\end{array}$$ Using the second expression, we can solve for $a$, $c$, and $d$ in terms of $b$: $$\begin{array}{rl}a& =2b-4,\\ c& =3b-6,\\ d& =3b-9\end{array}$$ Putting these values into the first equation gives $2b-4+b+3b-6+3b-9=35$, so $b=6$. Because $a=2b-4$, $a=12-4=\boxed{8}$.