Problem:
Harold made a plum pie to take on a picnic. He was able to eat only of the pie, and he left the rest for his friends. A moose came by and ate of what Harold left behind. After that, a porcupine ate of what the moose left behind. How much of the original pie still remained after the porcupine left?
Answer Choices:
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Solution:
Harold ate of the pie, so he left behind of the pie. The moose ate of the
remainder, so it ate of the pie, leaving behind of the pie. Finally, the porcupine ate of the remainder, so it ate of the pie, leaving behind of the original pie.
Harold left behind of the pie, the moose left behind of the remainder, and the porcupine left behind of that remainder. So the total fraction of the original pie that remained after the porcupine left was
Suppose the plum pie is cut into equal slices. Harold ate slices, leaving slices. Then the moose ate slices, leaving slices. Then the porcupine ate slices, leaving slices. Thus of the original pie remained after the porcupine left.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions