SOLUTION: A book is opened to a page at random. The product of the facing page numbers is 3422 . The sum of the facing page numbers is

Question 1185012: A book is opened to a page at random. The product of the facing page numbers is 3422 .
The sum of the facing page numbers is
Found 2 solutions by greenestamps, Alan3354:
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

Let the two page numbers be n and n+1. Note that to be page numbers in a book, the page number on the right should be odd, so n should be even and n+1 odd.

Algebraically, we would need to solve the equation

However, trying to solve that algebraically would lead to having to find two numbers that differ by 1 and whose product is 3422. But that's what the original problem asked us to do -- so the formal algebra doesn't help us.

Instead we can find the answer by trial and error, but with logical analysis.

The two numbers differ by 1, so the product 3422 is close to a perfect square; a "nice" perfect square close to 3422 is 60^2=3600. So the two numbers n and n+1 should be just under 60.

And to get a product with units digit 2 by multiplying two consecutive integers that are a bit less than 60, the only possibility is 58*59. And performing that calculation confirms that the product is indeed 3422.

So the two page numbers are 58 and 59.

ANSWER: The sum of the two page numbers is 58+59=117

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
A book is opened to a page at random. The product of the facing page numbers is 3422 .
The sum of the facing page numbers is
----------------
=~ 58.5
--> 58 & 59
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