Professor's Disease
Recently, a new store owner asked for help in reversecalculating a price so that the final amount charged was a "nice" number.
I wrote: "Suppose X is the cost of the item, Y is the 'revised' amount you will sell the item for, and the tax rate is R. Then, Y = X/(1+R)...rounded down to nearest cent.
For example, if the tax rate is 0.085 and the cost of the item is $100, then
y = 100/(1+.085) = 92.16589..., which rounded down is $92.16.
She wrote back: "I'll try this at work. I don't have a calculator here...... Thank you...... So, you take 1 + .085?"
I responded: "If .085 is your current tax rate... and then divide the item's price by that sum (i.e. 1+.085). To check it out, try your hand at these amounts...If you price an item at $5 or $25, the resultant prices charged are $4.60 or $23.04 respectively."
Two months later she responded: "I need help!!! My friend here says you have the "professor's disease" because you don't explain how you got the answers (4.60 and 23.04)....I'm still trying to figure this out....."
So, I responded: "Not sure how I could be much clearer, as the explanation was there if it was read (an assumption on my part).... Thus, have your friend reread the first line and follow instructions....which tells you to 'divide the item's price by that sum (i.e. 1+0.085)'....
So, for the given the amounts of $5 and $25,
5/1.085 = 4.6083 and 25/1.085 = 23.0415
which rounded down to twodecimal places becomes $4.60 and $23.04."
So, while I go ask my family doctor to run tests on my "professor's disease," perhaps I understand better why items end up being priced at 0.99¢.
