Algebra II: Word Problem #2

Question

There is an election for two open positions in an organization: president and vice-president. There are 380 ways it could turn out. How many people are up for those spots?

Answer 1

If you assume that the President position can be filled in n ways and then the VP n-1 ways, then

n² - n = 380

and the quadratic formula gives 20  as the answers (plus an extraneous root).