# 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

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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 2017 AMC 10A (Problems • Answer Key • Resources) Preceded byProblem 1 Followed byProblem 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 (Problems • Answer Key • Resources) Preceded byFirst Problem Followed byProblem 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