Dividing Fractions · Superchallenge problem

A pancake recipe uses $\dfrac{2}{3}$ cup of milk for every $\dfrac{3}{4}$ cup of flour. Lucy has $2\tfrac{1}{2}$ cups of milk and $3$ cups of flour. She makes as much batter as she can while keeping exactly the recipe's amounts of milk and flour in balance. How many cups of flour does she use? Give your answer as an improper fraction.