Problem:
Hui is an avid reader. She bought a copy of the bestseller Math is Beautiful. On the first day, Hui read 51​ of the pages plus 12 more, and on the second day she read 41​ of the remaining pages, plus 15 pages. On the third day, she read 31​ of the remaining pages, plus 18 pages. She then realized that there were only 62 pages left to read, which she read the next day. How many pages are in this book?
Answer Choices:
A. 120
B. 180
C. 240
D. 300
E. 360
Solution:
Reason backward as follows. On the third day, Hui reads 31​ of the remaining pages plus 18 more, leaving her with 62 pages left to read. This means that 62+18=80 is 32​ of the number of pages remaining at the end of the second day. She had 23​×80=120 pages left to read at the end of the second day. On the second day she read 41​ of the remaining pages plus 15 more, so 120+15=135 is 43​ of the number of pages remaining at the end of the first day. She had 34​×135=180 pages left to read at the end of the first day. On the first day she read 51​ of the pages plus 12 more. So 180+12=192 is 54​ of the number of pages in the book. The total number of pages is 45​×192=240.
OR
Setup a chart working backwards through the days, to show the number of pages that Hui has left to read each day.
Day4321​Extra Pages Read0181512​Fraction Read31​41​51​​Fraction Left32​43​54​​Calculation2/362+18​3/4120+15​4/5180+12​​Pages to be Read62120180240​​
Answer: C​.
The problems on this page are the property of the MAA's American Mathematics Competitions