The Dilemma of Drink Tickets

As part of the requirements of a seminar, I had to create an assignment for a mathematics class. Thanks to Song of Joy for the inspiration. If you can impress me with a solution to the scenario below, I will search you out and give you a prize for engaging in mathematics for leisure! Only one prize will be awarded. Contest closes in one week. Here goes!

The Scenario:

Anne works for a prominent hotel in the city. She is a catering manager. It is her job to oversee the many events that occur in the hotel’s banquet or conference rooms. Anne also needs to report the cost of the event, including all applicable taxes and gratuity. The cost can include items such as room rental, meal costs, and cash bars. However, the cash bar has been causing her some problems. Why? When a person picks up a drink at the bar, he or she often gives the bartender a drink ticket. The drink tickets cost a flat rate such as $4.00. This $4.00 includes all taxes and gratuity. When Anne records the cost of the drink for accounting purposes, she cannot just report $4.00. She needs to calculate what the original cost of the drink was before taxes and gratuity. Then, she has to show how the original cost of the drink plus all taxes and gratuity add up to $4.00.

Consider the following data:

  • GST rate is 5% of the original cost of the drink.
  • Liquor tax rate is 10% of the original cost of the drink.
  • Gratuity is 16% of the original cost of the drink.
  • GST has to be charged on gratuity (i.e. 5% of 16% of the original cost of the drink).
Anne needs an effective and efficient method to determine the original cost of the drink given the total cost of the drink (after taxes and gratuity) and the data above. Your challenge is to determine a method that will minimize Anne’s time in calculating the original cost of the drink, GST, Liquor Tax, Gratuity, GST on Gratuity, and the total cost of the drink (i.e. the cost of the drink ticket). Your method should accommodate changing tax and/or gratuity rates.

Impress me!

Note: The intention of this assignment is NOT to promote drinking at the high school level, but rather to illustrate that mathematics is used in the service industry. Of course, the topic of alcohol will peak some interest in the minds of students, thereby heightening their engagement in the scenario. To counteract any negative connotations, the assignment would include a disclaimer that the legal drinking age in our region is 19 years of age. Furthermore, the students would be encouraged to avoid drinking and driving.

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