A student opens a literature book to two facing pages. The product of the page numbers is 812. Find the page numbers

Question

A student opens a literature book to two facing pages. The product of the page numbers is 812. Find the page numbers  

Answer 1

Pages that are facing each other have page numbers that are consecutive.

 

Let one page number= x

Let the other page number = x + 1

 

Set up the equation using this information.

 

x(x + 1) = 812

x² + x = 812

 

Subtract 812 on both sides of the equation to have the right side equal to zero.

 

x² + x - 812 = 0

 

 

Lets use the quadratic formula:

 

x = (-b ± √(b² - 4ac)) / 2a

 

where:

a = 1

b = 1

c = -812

 

x = (-1 ± √(1 - 4(-812))) / 2

x = (-1 ± √(1 + 3248)) / 2

x = (-1 ± 57) / 2

 

x = (-1 + 57) / 2

x = (-1 - 57) / 2

 

x = -29

x = 28

 

Accept the positive value of x, since page numbers are only positive.

 

The two pages numbers are 28 and 29.