jmc

Suppose Sasha has $q$ quarters. Then she also has $q$ nickels, and the total value of her quarters and nickels is $.25q+.05q=.30q$. Since $3.20/0.30=10\frac{2}{3}$, this means that she has at most $\boxed{10}$ quarters. (This amount is obtainable; for example we can let the rest of her coins be pennies.)