2017 AMC 12A Problems/Problem 1

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. $\boxed{\textbf{D}}$ .

2016 AMC 10A (Problems • Answer Key • Resources)
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2016 AMC 12A (Problems • Answer Key • Resources)
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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2017 AMC 12A Problems/Problem 1

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