# A book is lying open on a desk. The product of the page numbers is 930. What are the two page numbers?

May 20, 2018

30 and 31

#### Explanation:

if the smaller number is x, then the larger number is x + 1
so their product is 930
i.e. x(x + 1) = 930
giving ${x}^{2}$ + x - 930 = 0
this factorises as (x +31)(x - 30) = 0
so x = 30 or x = -31
So the numbers are x = 30 and x + 1 = 31
Note the other solution if you work with integers. -31 and -30.
Their product is also 930
So if you work with Natural numbers there is one solution,
if you work with integers there are two solutions.