Problem:
Al, Bert, and Carl are the winners of a school drawing for a pile of Halloween candy, which they are to divide in a ratio of , respectively. Due to some confusion they come at different times to claim their prizes, and each assumes he is the first to arrive. If each takes what he believes to be his correct share of candy, what fraction of the candy goes unclaimed?
Answer Choices:
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E.
Solution:
Al, Bert, and Carl are to receive, respectively, , and of the candy. However, each believes he is the first to arrive. Therefore they leave behind, respectively, , and of the candy that was there when they arrived. The amount of unclaimed candy is of the original amount, regardless of the order in which they arrive.
The problems on this page are the property of the MAA's American Mathematics Competitions