I spent a couple of hours going over thermodynamics with a fellow physics major today. When the bill for my food came, I looked at it for a while as I calculated the tip. “Too much math, eh?” asked Alice, as I took a while to figure the thing out. I explained to her my process for deciding a tip, and she seemed to think it was rather complicated. I present it here for your edification.
Suppose your bill comes to a total of x. Choose an arbitrary whole dollar amount for the tip; let this value to be ‘t’. Calculate the the values 5t and 6t. These are the lower and upperbounds on hypothetical bill totals where ‘t’ would represent a 20% and 16.7% tip, respectively. If 5t < x < 6t, t is somewhere between 16.7% and 20% of the bill, and therefore an acceptable tip. If 6t > x, your tip is less than 16.6% and you should maybe choose a new one. Add one dollar to the tip and increase the upperbound by 6, then reverify. If x < 5t, the tip is larger than 20% and you might consider lessening a bit.
Whatever you may think, this system works well for me, and I don’t have to mess with any nasty decimals.