AMC12 2017 12A, Problem 1

Pablo buys popsicles for his friends. The store sells single popsicles for \[1$ each, 3-popsicle boxes for \]2$, and 5-popsicle boxes for \[3$. What is the greatest number of popsicles that Pablo can buy with \]8$?

Solution: We can take two 5-popsicle boxes and one 3-popsicle box with \[8$. Note that it is optimal since one popsicle is at the rate of \]1$ per popsicle, three popsicles at \[\frac{2}{3}$ per popsicle and finally, five popsicles at \]\frac{3}{5}$ per popsicle, hence we want as many $$3$ sets as possible. It is clear that the above is the optimal method. $\fbox{13}$.

Answer: 13