jmc

We let $x$ denote the number of slips with a 2 written on them. (This is the usual tactic of letting a variable denote what we're trying to solve for in the problem.) Then there are $12-x$ slips with a 7 on them. The probability of drawing a 2 is $\frac{x}{12}$ and the probability of drawing a 7 is $\frac{12-x}{12}$, so the expected value of the number drawn is $$E=\frac{x}{12}(2)+\frac{12-x}{12}(7)=\frac{84-5x}{12}.$$But we are given that $E=3.25$, so we have the equation $$3.25=\frac{84-5x}{12}.$$This simplifies to $39=84-5x$, which means that $x=9$. Thus $\boxed{9}$ of the 12 slips have a 2 written on them.