algebra 2 word problem

Question

If a switchboard handles (n) telephones, the number (c) of telephone connections it can make simultaneously is given by the equation C=n(n-1)/2. find how many telephones are handled by switchboard making 120 connections simultaneously?

Answer 1

240= n(n-1)

 

240= n^2 - n

 

0 = n^2 - n - 240

 

0 = (  n      +  16)(n  -     15 )

 

n+16 = 0 --> n = -16  <--- rejected

 

n - 15 = 0 --> n = 15

 

15 phone lines can be handled by 16*15/2 = 120 phone lines