Answer to April 2008 Problem of the Month

CiCi Pizza Problem

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Mrs. P and I ate at the new pizza place in town called CiCi's.   The menu consists of two items: (1) All you can eat pizza, pasta, salad, and dessert for $4.99, and (2) All you can drink beverage for $1.49.   The bill for our lunch (2 buffets and 2 drinks) was $13.83 which included the tax.   What is the tax rate here in our town of Fort Collins?

We noticed that most of the patrons were high school and college students and that they received a discount by showing their school ID.   The total bill for the student in front of us was $5.88.   What discount did the students get (what % off did they receive?)?

 

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Solution to the Problem:

The tax rate is 6.7% and the student discount is 15%.

We paid $12.96 plus 87 cents tax for our lunch for two.
Therefore, the tax rate is .87 / 12.96 = .067 = 6.7%.

Since the total bill for the student was $5.88,
the bill for her buffet and drink was $5.51.
Let x = charge for her buffet and drink.
Then x + .067x = 5.88.
So, 1.067x = 5.88, and x = 5.51.
Since my wife and I each were charged $6.48 for our buffet and drink,
the students got a discount of 6.48 - 5.51 = .97.
So, the discount rate for students is .97 / 6.48 = .14969 = 15%.