Problem:
Hui is an avid reader. She bought a copy of the bestseller Math is Beautiful. On the first day, Hui read of the pages plus more, and on the second day she read of the remaining pages, plus pages. On the third day, she read of the remaining pages, plus pages. She then realized that there were only pages left to read, which she read the next day. How many pages are in this book?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Reason backward as follows. On the third day, Hui reads of the remaining pages plus more, leaving her with pages left to read. This means that is of the number of pages remaining at the end of the second day. She had pages left to read at the end of the second day. On the second day she read of the remaining pages plus more, so is of the number of pages remaining at the end of the first day. She had pages left to read at the end of the first day. On the first day she read of the pages plus more. So is of the number of pages in the book. The total number of pages is .
Setup a chart working backwards through the days, to show the number of pages that Hui has left to read each day.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions