2008 AMC 12A Problem 3

Since $\tfrac{2}{3}$ of $10$ bananas is $\tfrac{20}{3}$ bananas, worth $8$ oranges, one banana is worth $$8 \div \dfrac{20}{3} = \dfrac{24}{20} = \dfrac{6}{5}$$ oranges. Then $\tfrac{1}{2}$ of $5$ bananas is $\tfrac{5}{2}$ bananas, worth $$\dfrac{5}{2} \cdot \dfrac{6}{5} = 3$$ oranges. Thus, C is the correct answer.