2017 AMC 12A Problems/Problem 1
Problem
Pablo buys popsicles for his friends. The store sells single popsicles for each, 3-popsicle boxes for
, and 5-popsicle boxes for
. What is the greatest number of popsicles that Pablo can buy with
?
Solution
By the greedy algorithm, we can take two 5-popsicle boxes and one 3-popsicle box with . To prove that this is optimal, consider an upper bound as follows: at the rate of
per 5 popsicles, we can get
popsicles, which is less than 14.
.