1961 AHSME Problems/Problem 24
Problem 24
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 the adjacent one. Then:
Solution
Let the leftmost book cost dollars. The 16th book (the middle book) costs dollars, and the 31st book costs dollars.
If the book to the left of the middle book is used, the equation to solve for the price of the leftmost book is . Solving yields , so the price of the middle book is and the price of the rightmost book is .
If the book to the right of the middle book is used, the equation to solve for the price of the leftmost book is . Solving yields , which can not happen.
Thus, the answer is .
See Also
1961 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 23 |
Followed by Problem 25 | |
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