Difference between revisions of "2017 AMC 12A Problems/Problem 1"

Latest revision as of 06:03, 14 September 2024

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

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

Video Solution (HOW TO THINK CREATIVELY!!!)

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Video Solution

https://www.youtube.com/watch?v=Ro_koxVqd50

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2017 AMC 10A (Problems • Answer Key • Resources)
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All AMC 10 Problems and Solutions

2017 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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