The product of two consecutive room numbers is 132. Find the room number.

Question

The number of the first room, or the smaller room number, is 

Answer 1

Let's first assign some variables. Let the first room be a and the second room be a+1 (so that it is consecutive. 

 

a * (a+1) = 132. 

 

a² + a = 132

a² + a - 132= 0

 

Factor

(a+12)(a-11) = 0

a=-12, a=11

 

We can rule out the -12 because room numbers are not negative. 

 

The room number is #11. 

Answer 2

(n)(n + 1) = 132

 

Can you solve for n and answer?