Simultaneous equations word problem

Question

When Bob opens a business mathematics textbook, he realizes that the product of two page numbers he is looking at is 2652. What are the two page numbers that Bob is looking at? (Hint: you have to use an equation(s) to solve this problem)

Answer 1

Bob can see two consecutive pages: n,n+1

n(n+1)=2652

n²+n=2652

n=51. 

So pages are 51 and 52

 

Answer 2

let us assume that one of page = x

therefore other page would be = x+1  

 

x(x+1) = 2652

 

x^2 +x = 2652

 

x^2+x - 2652 =0

 

x^2 +52x-51x -2652 =0

x(x+52) -51(x+52)=0

(x+52)(x-51) = 0

 

therefore the pages bob is looking at are 51 and 52