Algebra? Really?

Here's a word problem for ya: A singer/songwriter is offered a gig with a choice of payment options. They are: - take a $450 guarantee versus 80% of the door less $150 for sound at an $8 ticket price - take 90% of the door less $150 for sound with no guarantee - take a flat $650 guarantee with no versus percentage If the singer/songwriter expects to pull in a crowd of 112 people, which deal is the best? We did an Excel spreadsheet with formulas today to figure out something like this. The numbers were completely different, but the formulas are the same. It made my head hurt. We think we picked the right deal.