Quandaries and Queries

You open a book and the product of the page numbers is 12,656. What are your page numbers?

Morgan and Mom
Age 14
8th grade

How do we come up with the answer?


When you open the book you see two page numbers, one on the left page and one on the right. These are two consecutive integers.

I can see two ways to solve this problem. If Morgan is studing quadratic equations in algebra then I would do the following.

Since the page numbers are consecutive integers I can call them n and n + 1. Then I know that n (n + 1) = 12,656. That is n2 + n - 12,656 = 0 Solve for n.

If Morgan isn't studing quadratic equations then you can solve this problem with some intellegent guess and check.

The two page numbers are very close (their difference is 1) and their product is 12,656. So, if you take one of the page numbers and multiply it by itself you should get something close to 12,656. Hence 12,656 is almost the square of one of the numbers. Use your calculator and take the square root of 12,656, I got 112.499. Hence my guess. One of the page numbers is 112 or maybe 113. Now check.

Did you actually look at a book? Once you know what the two page numbers are, can you say which is on the left page and which is on the right?


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