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2017 AMC 10A Problem 2

Problem 2 of 25EasierAlgebra

Pablo buys popsicles for his friends. The store sells single popsicles for $1\$1 each, 33-popsicle boxes for $2\$2 each, and 55-popsicle boxes for $3.\$3. What is the greatest number of popsicles that Pablo can buy with $8?\$8?

Answer choices

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Solution

The $3\$3 boxes give us the most popsicles per dollar, so we want to buy as many of those as possible. We can buy two of those, getting 52=105 \cdot 2 = 10 popsicles with $8$6=$2\$8 - \$6 = \$2 remaining. The $1\$1 single popsicles are the worst deal, so Pablo should spend the rest of his money on the 33-popsicle box. He then ends up with 10+3=1310 + 3 = 13 popsicles. Thus, D is the correct answer.

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Concepts: money · optimization

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.