SOLUTION: Megan opens her math book to a random page. The page numbers she can see multiply to 756. Find the sum of these numbers.

Question 1209225: Megan opens her math book to a random page. The page numbers she can see multiply to 756. Find the sum of these numbers.
Found 3 solutions by math_tutor2020, ikleyn, greenestamps:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

x = page number on the left
x+1 = page number on the right
x*(x+1) = product of those numbers
x*(x+1) = 756 is one possible starting equation

Do a bit of algebra to convert it to x^2+x-756 = 0.
Compare that to ax^2+bx+c = 0 to find a = 1, b = 1, c = -756

Those items are then plugged into the quadratic formula
I'll let the student handle the scratch work.
The solutions are x = -28 and x = 27.

Ignore the negative value. A negative page number isn't allowed.
x = 27 leads to x+1 = 27+1 = 28.
The two pages are 27 and 28
27*28 = 756
27+28 = 55 is the final answer.

Answer by ikleyn(52880)   (Show Source): You can put this solution on YOUR website!
.
Megan opens her math book to a random page. The page numbers she can see multiply to 756.
Find the sum of these numbers.
~~~~~~~~~~~~~~~~~~~~~

Traditionally and normally, numeration of pages in books is such that
in open book, the page on the left side has even number;
the page on the right side has odd number.

So, in traditional page numeration, even number of the page of an open book
is one less than the corresponding odd number.

Again, the traditional page numeration is this

left side right side even number next odd number

Tutor @math_tutor2020 got the answer in reverse order (27,28).

Formally, he solved the problem correctly, but it means that
in the book Megan opened, non-traditional numeration of pages is used.

Which creates many questions like THIS:

        "was the problem's creator in healthy mind, when he composed this problem ?"

Or, probably, the problem is stated incorrectly ?

-----------------------

It is not for the first time I notice such problems at the forum with
incorrect pages numeration.

First time, I saw it many years ago, and reacted correspondingly.

I even placed a lesson at this site
    - Page numbers on the left and right facing pages of an opened book
which teaches on how to formulate and how to solve such problems in a right way,
and how to detect / (to recognize) if the problem is posed incorrectly.

Read there and learn the subject.

Answer by greenestamps(13209)   (Show Source): You can put this solution on YOUR website!

The two page numbers are consecutive integers.

The product of two consecutive integers can be approximated as the square of an integer. Using that idea, we can find the two page numbers by logical trial and error, without formal algebra.

The given product of the two page numbers is 756; a perfect square close to that is 27^2 = 729, and 27*28 = 729+27 = 756, which is the given product.

So the two page numbers are 27 and 28.

But, as tutor @ikleyn points out (and has pointed out previously in similar problems) virtually always (if not ALWAYS) page numbers in a book are numbered so that the two page numbers showing when the book is open have the even-numbered page on the left and the odd-numbered page on the right.

So the problem is a good math problem only if you ignore the way that page numbers in a book are numbered.

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