Question

Lena is reading a book. The product of the two page numbers facing each other is 5852. What is the sum of the two pages?

Answer 1

first page is 12, and the facing page is 13.

Explanation:

The pages are facing each other, so they are consecutive numbers:

Let x = the first page number

y = the second page number

The second page number is just 1 more than the first, because they are consecutive numbers:

x+1 = y

We also know that the products of the numbers is equal to 156:

xy = 5852

Now we will sub y = x+1 into the second equation:

x(x+1) = 5852

x^2 + x = 5852

x^2 + x - 5852 = 0

Factoring (or using the quadratic formula) gives us:

(x+13)(x-12) = 0

x = - 13, or x = 12.

A page number can't be negative, so we will choose x=12.

This means that the second page must be page 13.