Problem: Thirty-one books are arranged from left to right in order of increasing prices. The price of each book differs by from that of each adjacent book. For the price of the book at the extreme right a customer can buy the middle book and an adjacent one. Then:
Answer Choices:
A. The adjacent book referred to is at the left of the middle book
B. The middle book sells for
C. The cheapest book sells for
D. The most expensive book sells for
E. None of these is correct
Solution:
Let the prices, arranged in order from left to right, be . The price of the middle book is . Then either or . The first equation yields a negative value for , an impossibility. The second equation leads to , so that is the correct choice.