2017 AMC 12A Problems/Problem 1

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Problem

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$?

$\textbf{(A)}\ 8\qquad\textbf{(B)}\ 11\qquad\textbf{(C)}\ 12\qquad\textbf{(D)}\ 13\qquad\textbf{(E)}\ 15$

Solution

By the greedy algorithm, we can take two 5-popsicle boxes and one 3-popsicle box with $$8$. To prove that this is optimal, consider an upper bound as follows: at the rate of $$3$ per 5 popsicles, we can get $\frac{40}{3}$ popsicles, which is less than 14. $\boxed{\textbf{D}}$.

See Also

2017 AMC 10A (ProblemsAnswer KeyResources)
Preceded by
Problem 1
Followed by
Problem 3
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AMC 10 Problems and Solutions
2017 AMC 12A (ProblemsAnswer KeyResources)
Preceded by
First Problem
Followed by
Problem 2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AMC 12 Problems and Solutions

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