What if people split a dinner check using the principles of the progressive income tax that is central to our tax code? Five lifelong friends of various means meet once a week for dinner and split the $100 check according to their ability to pay. Tom, Dick, and Harry are of relatively modest means and pay $1, $4, and $9, respectively. Ben and Ken are far more prosperous and pay $18 and $68, respectively.
The friends were quite satisfied with the arrangement until the owner offered a rebate. "You are excellent customers, and I will reduce the cost of your meal by $15." The question became how to divide the $15 windfall to give everyone his fair share? The proprietor suggested that they allocate the savings according to the amount each contributed to the original check. He made a quick calculation, and then rounded each person's share to an integer, using the Integer function. For example, Tom's new bill should have been 85 cents, but it was decided he would eat for free. In similar fashion, Dick now owes $3, Harry $7, Ben $15, and Ken $60. (Ken, the most prosperous individual, made up the difference with respect to the cents that were dropped.) The new total is $85, and everyone saves money.
Once outside the restaurant, the friends began to compare their savings. Tom and Dick each complained that they saved only $1. Harry grumbled that he saved only $2. Ben thought it unfair that Ken saved more than the other friends combined. Everyone continued to pick on Ken. The next week, Ken felt so uncomfortable that he did not show up, so his former friends ate without him. But when the bill came, they were $60 short.
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