Problem:
On Halloween Casper ate of his candies and then gave candies to his brother. The next day he ate of his remaining candies and then gave candies to his sister. On the third day he ate his final candies. How many candies did Casper have at the beginning?
Answer Choices:
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E.
Solution:
Let be Casper's original number of candies. After the first day he was left with candies. On the second day he ate candies, gave away candies, and was left with candies. Therefore
Solving for results in .
Before giving candies to his sister, Casper had . This was of the number he had after the first day, so he had after the first day. Before giving candies to his brother, he had , and this was of the number he had originally. Therefore he had candies at the beginning.
The problems on this page are the property of the MAA's American Mathematics Competitions